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MATHS TEST ON Probability 1.

(1) A dice is thrown once. Find the probability of getting (a) A number greater than 3 (b) A number less than 5 A. ½,2/3, 4/3, 2/3 B. 2/3, 4/3, 2/3 C. 4/3, 4/3, 2/3 D. 4/3, 2/3,13/8

2.

A bag contain 5 black, 7 red and 3 white balls. A ball is drawn from the bag at random. Find the probability that the ball drawn is (a) Red (b) Black or white (c) Not black A. 7/15 B. 8/15 C. 2/3

3.

D. 4/3 A bag contains 4 red 5 black and 6 white balls. A ball is drawn from the bag a random. Find the probability that the ball drawn is (a) White (b) Red (c) Not black (d) Red or white A. 2/5, 4/15, 2/3, 2/3 B. 4/3, 4/15, 1/3, 2/3 C. 4/15, 2/3, 2/3 1/3

4.

D. 4/15, 2/3, 4/3 2/3 A card is drawn at random from a pack of 52 playing cards. Find the probability that the card drawn is neither a queen nor a jack. A. 11/13 B. 12/13 C. 11/14

5.

D. 11/12 Tickets numbered from 1 to 20 are mixed up together and then a ticket is drawn at random. What is the probability that the ticket has a number which is a multiple of 3 or 7? A. 2/5 B. 2/3

C. 4/3 D. 2/3

6.

In a single throw of dice, what is the probability of (a) An odd number on one dice and 6 on the other (b) A number greater than 4 on each dice (c) A total of 11 (d) Getting same number on either dice. A. 1/6, 1/9, 1/18, 1/6 B. 1/6, 1/9, 2/18, 1/6 C. 1/6, 1/3, 1/18, 1/6 D. 1/6, 1/9, 7/18, 1/6

7.

A die is thrown twice. Find the probability of getting (a) doublets (b) number greater than 5 on one dice. A. 1/6, 11/36 B. 1/6, 11/7 C. 1/6, 11/6 D. 1/6, 11/3

8.

Three coins are tossed simultaneously. Find the probability of getting (a) Exactly 2 heads (b) No heads A. 2/8, 1/8 B. 3/8, 1/8 C. 3/8, 7/8 D. 4/3, 1/8

9.

In a simultaneous toss of four coins, What is the probability of getting: (a) Less than 2 heads? (b) Exactly 3 head (c) More than 2 heads? A. 5/6, 2/8, 5/16 B. 5/6, 3/8, 5/16 C. 5/6, 3/9, 5/16 D. 5/6, 3/4, 5/1

10. Three coins are tossed once. Find the probability of: (a) 3 heads

(b) exactly 2 heads (c) at least two heads A. 1/3, 3/8, 1/2 B. 1/8, 3/8, 1/9 C. 1/8, 3/8, 1/2 D. 1/8, 3/7, ½

11. A bag contains 5 red balls, 8 White balls, 4 green balls and 7 black balls. A ball is drawn at random from the bag. Fine the probability that it is. (i) Black (ii) not green. A.

2/3

B.

5/6

C.

3/8

D.

7/3

12. A card is drawn at random from a pack of 52 playing cards. Find the probability that the card drawn is neither an ace nor a king.

13.

A.

2/3

B.

11/13

C.

3/8

D.

7/3

An unbiased dice is tossed. 1.

Write the sample space of the experiment

2. 3.

Find the probability of getting a number greater than 4. Find the probability of getting a prime number. A.

6,2,2/3

B.

6,2,1/2

C.

6,2,2/3

D.

6,2,2/7

14. Out of 400 bulbs in a box, 15 bulbs a defective. One ball is taken out at random from the box. Find the probability that the drawn bulb is not defective.

A. B.

77/80 77/80

C. D.

77/80 77/80

15. Find the probability of getting 53 Fridays in a leap year.

a. b. c. d. 16.

1/7 2/7 3/7 4/7

Three unbiased coins are tossed simultaneously. What is the probability of getting

exactly two heads?

e. f. g. h.

3/8 4/8 3/7 4/7

17. A dice is thrown twice. Find the probability of getting (a) doublets (b) prime number on each die.

i. j. k. l.

3/8 1/4 3/4 2/4

18 One card is drawn from a well shuffled pack of 52 cards. probability of drawing. (i) an ace (ii) 2 of spades (iii) 10 of black suit (iv)a hearts m. n. o. p.

Find the king

1/13,1/13,1/13,1/13 1/13,2/13,1/13,1/13 1/13,1/13,3/13,1/13 1/13,1/13,1/13,4/13

One card is drawn from a well shuffled deck of 52 cards calculate the probability that the card will a) not be an ace b) be an ace 19.

q.

12/13,1/13

r. s.

2/13,1/13 2/26,1/13

t.

2/13,1/52

of

Find the probability of getting Monday or Tuesday in a leap year.

20.

u.

1/2

v. 2/7 w. 1/7 x.

2/14

From a group of 3 boys and 5 girls, a child is to be selected for the competition. Find the probability that the selected child is ( i ) a boy ( ii ) a girl.

21.

y. 3/8,5/8 z. 3/5,8/3 aa. 8/5,4/3 bb. 1/13,1/13 22.

In a single throw of two dice , find the probability of getting i) Two heads

23.

ii) At least one heads

cc. ¼,3/4 dd. 2/4,3/4 ee. ¼,1/2 ff. ¾,3/4 What is probability of choosing the red ball from a box containing 20 balls if it is having equal number of yellow, red, blue and green balls? gg. 5/20 hh. ¼ ii. ½ jj. 1/4

There are three children in a family. Find the probability that there is one girl in the family. 24.

kk. 1/3 ll. ¼ mm.½ nn. 1

25. One card is drawn from a well shuffled deck of 52 cards. Calculate the probability that the card drawn will be an ace. a. 1/13 b. 4/13 c. 13/52 d. 13/52

Answers 1. 1/2, 2/3,

2. 7/15, 8/15, 2/3

3. 2/5, 4/15, 2/3, 2/3

4. 11/13,

5. 2/5

6. 1/6, 1/9, 1/18, 1/6

7. 1/6, 11/36

8. 3/8, 1/8

9. 5/6, 3/8, 5/16

10. 1/8, 3/8, 1/2

11. 5/6

12.

13.

6,2,1/2

14.

77/80

15.

2/7

11/13

16. 3/8

17.1/13,1/13,1/13,1/13 18.1/13,1/13,1/13,1/13 19. 2/13,1/13

20.2/7

21.1/4,3/4

24

221/4,3/4

231/4

25.1/13

11. An unbiased dice is tossed. 26. Write the sample space of the experiment 27. Find the probability of getting a number greater than 4. 28. Find the probability of getting a prime number. Solution:-

1.

Sample space = {1, 2, 3, 4, 5, 6} n(s) = 6

2.

E = event of getting a number greater than 4 = {5, 6}

n (E) = 2 P (> 4) = Probability of a number greater than 4 = n(E)/n(S) = 2/6 = 1/3 3.

E = Event of getting a prime number = {2, 3, 5} n (E) = 3 P(Prime number) = Probability of a prime number

12. Out of 400 bulbs in a box, 15 bulbs a defective. One ball is taken out at random from the box. Find the probability that the drawn bulb is not defective. Solution:- Total number of bulbs = 400 Total number of defective bulb = 15 Total number of non-defective bulbs = 400-15 = 385 P (not defective bulb) = 385/400 = 77/80 13. Find the probability of getting 53 Fridays in a leap year. Solution:- No. of days in a leap year = 366 366 days = 52 weeks and 2 days. A leap year must has 52 Fridays The remaining two days can be (a) Sunday an Monday (b) Monday and Tuesday (c) Tuesday and Wednesday (d) Wednesday and Thursday

(e) Thursday and Friday (f) Friday and Saturday (g) Saturday and Sunday Out of 7 case, 2 cases have Friday P (53 Friday) = 2/7

14. Three unbiased coins are tossed simultaneously. What is the probability of getting exactly two heads? Solution: - When three coins are tossed simultaneously, the sample space is S = {HHH, HHT, HTH, THH, HTT, THT, TTH, TTT}. n(S) = 8 E = Set of cases favorable to the event = {HHT, HTH, THH} n(E) = 3

P (exactly two heads) = 15.. A dice is thrown twice. Find the probability of getting (a) doublets (b) prime number on each die. Solutions: - Sample space = S = { (1, 1) (1, 2) (1, 3) (1, 4) (1, 5) (1, 6) (2, 1) (2, 2) (2, 3) (2, 4) (2, 5) (2, 6) (3, 1) (3, 2) (3, 3) (3, 4) (3, 5) (3, 6) (4, 1) (4, 2) (4, 3) (4, 4) (4, 5) (4, 6) (5, 1) (5, 2) (5, 3) (5, 4) (5, 5) (5, 6) (6, 1) (6, 2) (6, 3) (6, 4) (6, 5) (6, 6) } n (S) = 36

(i) E = Events getting doublet = {(1, 1) (2, 2) (3, 3) (4, 4) (5, 5) (6, 6)} n (E) = 6

P(doublet) = (ii) E = Events getting prime number on each die. = {(2, 2), (2, 3), (2, 5), (3, 2), (3, 3), (3, 5), (5, 2), (5, 3), (5, 5)} n(E) = 9 P (getting prime number on each die) = n(E)/n(S) = 9/36 = 1/4

16. A bag contains 5 red balls, 8 White balls, 4 green balls and 7 black balls. A ball is drawn at random from the bag. Fine the probability that it is. (i) Black (ii) not green. Solution:- Red balls = 5 White balls = 8 Green balls = 4 Black balls = 7 Total balls = 24 (i) P (Black balls) = 7/24 (ii) P (not a green ball) = 1- P (green ball) = 1 - 4/24 = 20/24 = 5/6 17. A card is drawn at random from a pack of 52 playing cards. Find the probability that the card drawn is neither an ace nor a king. Solution:- P (neither an ace nor a king) = 1 – p (either an ace or a king)

= 1 – 8/52

{no. of ace = 4} {no. of king = 4} Total = 8

= (52 – 8)/52 = 44/52 = 11/13

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(1) A dice is thrown once. Find the probability of getting (a) A number greater than 3 (b) A number less than 5 A. ½,2/3, 4/3, 2/3 B. 2/3, 4/3, 2/3 C. 4/3, 4/3, 2/3 D. 4/3, 2/3,13/8

2.

A bag contain 5 black, 7 red and 3 white balls. A ball is drawn from the bag at random. Find the probability that the ball drawn is (a) Red (b) Black or white (c) Not black A. 7/15 B. 8/15 C. 2/3

3.

D. 4/3 A bag contains 4 red 5 black and 6 white balls. A ball is drawn from the bag a random. Find the probability that the ball drawn is (a) White (b) Red (c) Not black (d) Red or white A. 2/5, 4/15, 2/3, 2/3 B. 4/3, 4/15, 1/3, 2/3 C. 4/15, 2/3, 2/3 1/3

4.

D. 4/15, 2/3, 4/3 2/3 A card is drawn at random from a pack of 52 playing cards. Find the probability that the card drawn is neither a queen nor a jack. A. 11/13 B. 12/13 C. 11/14

5.

D. 11/12 Tickets numbered from 1 to 20 are mixed up together and then a ticket is drawn at random. What is the probability that the ticket has a number which is a multiple of 3 or 7? A. 2/5 B. 2/3

C. 4/3 D. 2/3

6.

In a single throw of dice, what is the probability of (a) An odd number on one dice and 6 on the other (b) A number greater than 4 on each dice (c) A total of 11 (d) Getting same number on either dice. A. 1/6, 1/9, 1/18, 1/6 B. 1/6, 1/9, 2/18, 1/6 C. 1/6, 1/3, 1/18, 1/6 D. 1/6, 1/9, 7/18, 1/6

7.

A die is thrown twice. Find the probability of getting (a) doublets (b) number greater than 5 on one dice. A. 1/6, 11/36 B. 1/6, 11/7 C. 1/6, 11/6 D. 1/6, 11/3

8.

Three coins are tossed simultaneously. Find the probability of getting (a) Exactly 2 heads (b) No heads A. 2/8, 1/8 B. 3/8, 1/8 C. 3/8, 7/8 D. 4/3, 1/8

9.

In a simultaneous toss of four coins, What is the probability of getting: (a) Less than 2 heads? (b) Exactly 3 head (c) More than 2 heads? A. 5/6, 2/8, 5/16 B. 5/6, 3/8, 5/16 C. 5/6, 3/9, 5/16 D. 5/6, 3/4, 5/1

10. Three coins are tossed once. Find the probability of: (a) 3 heads

(b) exactly 2 heads (c) at least two heads A. 1/3, 3/8, 1/2 B. 1/8, 3/8, 1/9 C. 1/8, 3/8, 1/2 D. 1/8, 3/7, ½

11. A bag contains 5 red balls, 8 White balls, 4 green balls and 7 black balls. A ball is drawn at random from the bag. Fine the probability that it is. (i) Black (ii) not green. A.

2/3

B.

5/6

C.

3/8

D.

7/3

12. A card is drawn at random from a pack of 52 playing cards. Find the probability that the card drawn is neither an ace nor a king.

13.

A.

2/3

B.

11/13

C.

3/8

D.

7/3

An unbiased dice is tossed. 1.

Write the sample space of the experiment

2. 3.

Find the probability of getting a number greater than 4. Find the probability of getting a prime number. A.

6,2,2/3

B.

6,2,1/2

C.

6,2,2/3

D.

6,2,2/7

14. Out of 400 bulbs in a box, 15 bulbs a defective. One ball is taken out at random from the box. Find the probability that the drawn bulb is not defective.

A. B.

77/80 77/80

C. D.

77/80 77/80

15. Find the probability of getting 53 Fridays in a leap year.

a. b. c. d. 16.

1/7 2/7 3/7 4/7

Three unbiased coins are tossed simultaneously. What is the probability of getting

exactly two heads?

e. f. g. h.

3/8 4/8 3/7 4/7

17. A dice is thrown twice. Find the probability of getting (a) doublets (b) prime number on each die.

i. j. k. l.

3/8 1/4 3/4 2/4

18 One card is drawn from a well shuffled pack of 52 cards. probability of drawing. (i) an ace (ii) 2 of spades (iii) 10 of black suit (iv)a hearts m. n. o. p.

Find the king

1/13,1/13,1/13,1/13 1/13,2/13,1/13,1/13 1/13,1/13,3/13,1/13 1/13,1/13,1/13,4/13

One card is drawn from a well shuffled deck of 52 cards calculate the probability that the card will a) not be an ace b) be an ace 19.

q.

12/13,1/13

r. s.

2/13,1/13 2/26,1/13

t.

2/13,1/52

of

Find the probability of getting Monday or Tuesday in a leap year.

20.

u.

1/2

v. 2/7 w. 1/7 x.

2/14

From a group of 3 boys and 5 girls, a child is to be selected for the competition. Find the probability that the selected child is ( i ) a boy ( ii ) a girl.

21.

y. 3/8,5/8 z. 3/5,8/3 aa. 8/5,4/3 bb. 1/13,1/13 22.

In a single throw of two dice , find the probability of getting i) Two heads

23.

ii) At least one heads

cc. ¼,3/4 dd. 2/4,3/4 ee. ¼,1/2 ff. ¾,3/4 What is probability of choosing the red ball from a box containing 20 balls if it is having equal number of yellow, red, blue and green balls? gg. 5/20 hh. ¼ ii. ½ jj. 1/4

There are three children in a family. Find the probability that there is one girl in the family. 24.

kk. 1/3 ll. ¼ mm.½ nn. 1

25. One card is drawn from a well shuffled deck of 52 cards. Calculate the probability that the card drawn will be an ace. a. 1/13 b. 4/13 c. 13/52 d. 13/52

Answers 1. 1/2, 2/3,

2. 7/15, 8/15, 2/3

3. 2/5, 4/15, 2/3, 2/3

4. 11/13,

5. 2/5

6. 1/6, 1/9, 1/18, 1/6

7. 1/6, 11/36

8. 3/8, 1/8

9. 5/6, 3/8, 5/16

10. 1/8, 3/8, 1/2

11. 5/6

12.

13.

6,2,1/2

14.

77/80

15.

2/7

11/13

16. 3/8

17.1/13,1/13,1/13,1/13 18.1/13,1/13,1/13,1/13 19. 2/13,1/13

20.2/7

21.1/4,3/4

24

221/4,3/4

231/4

25.1/13

11. An unbiased dice is tossed. 26. Write the sample space of the experiment 27. Find the probability of getting a number greater than 4. 28. Find the probability of getting a prime number. Solution:-

1.

Sample space = {1, 2, 3, 4, 5, 6} n(s) = 6

2.

E = event of getting a number greater than 4 = {5, 6}

n (E) = 2 P (> 4) = Probability of a number greater than 4 = n(E)/n(S) = 2/6 = 1/3 3.

E = Event of getting a prime number = {2, 3, 5} n (E) = 3 P(Prime number) = Probability of a prime number

12. Out of 400 bulbs in a box, 15 bulbs a defective. One ball is taken out at random from the box. Find the probability that the drawn bulb is not defective. Solution:- Total number of bulbs = 400 Total number of defective bulb = 15 Total number of non-defective bulbs = 400-15 = 385 P (not defective bulb) = 385/400 = 77/80 13. Find the probability of getting 53 Fridays in a leap year. Solution:- No. of days in a leap year = 366 366 days = 52 weeks and 2 days. A leap year must has 52 Fridays The remaining two days can be (a) Sunday an Monday (b) Monday and Tuesday (c) Tuesday and Wednesday (d) Wednesday and Thursday

(e) Thursday and Friday (f) Friday and Saturday (g) Saturday and Sunday Out of 7 case, 2 cases have Friday P (53 Friday) = 2/7

14. Three unbiased coins are tossed simultaneously. What is the probability of getting exactly two heads? Solution: - When three coins are tossed simultaneously, the sample space is S = {HHH, HHT, HTH, THH, HTT, THT, TTH, TTT}. n(S) = 8 E = Set of cases favorable to the event = {HHT, HTH, THH} n(E) = 3

P (exactly two heads) = 15.. A dice is thrown twice. Find the probability of getting (a) doublets (b) prime number on each die. Solutions: - Sample space = S = { (1, 1) (1, 2) (1, 3) (1, 4) (1, 5) (1, 6) (2, 1) (2, 2) (2, 3) (2, 4) (2, 5) (2, 6) (3, 1) (3, 2) (3, 3) (3, 4) (3, 5) (3, 6) (4, 1) (4, 2) (4, 3) (4, 4) (4, 5) (4, 6) (5, 1) (5, 2) (5, 3) (5, 4) (5, 5) (5, 6) (6, 1) (6, 2) (6, 3) (6, 4) (6, 5) (6, 6) } n (S) = 36

(i) E = Events getting doublet = {(1, 1) (2, 2) (3, 3) (4, 4) (5, 5) (6, 6)} n (E) = 6

P(doublet) = (ii) E = Events getting prime number on each die. = {(2, 2), (2, 3), (2, 5), (3, 2), (3, 3), (3, 5), (5, 2), (5, 3), (5, 5)} n(E) = 9 P (getting prime number on each die) = n(E)/n(S) = 9/36 = 1/4

16. A bag contains 5 red balls, 8 White balls, 4 green balls and 7 black balls. A ball is drawn at random from the bag. Fine the probability that it is. (i) Black (ii) not green. Solution:- Red balls = 5 White balls = 8 Green balls = 4 Black balls = 7 Total balls = 24 (i) P (Black balls) = 7/24 (ii) P (not a green ball) = 1- P (green ball) = 1 - 4/24 = 20/24 = 5/6 17. A card is drawn at random from a pack of 52 playing cards. Find the probability that the card drawn is neither an ace nor a king. Solution:- P (neither an ace nor a king) = 1 – p (either an ace or a king)

= 1 – 8/52

{no. of ace = 4} {no. of king = 4} Total = 8

= (52 – 8)/52 = 44/52 = 11/13

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