Exercise for HKDSE(More about Probability)(5).pdf

HKDSE Exercise

MATHEMATICS (Core)

By HENRY LEUNG

HKDSE Mathematics Exercise Topic: More about Probability 1. Charis forgot the last 2 digits of his friend's phone number, she only recalled that each of the two digits is in the range from 1 to 5 . a) What is the probability that she can call her friend by phone in the first attempt? b) What is the probability that the two digits are one is odd and another is even? 2. If a four digit number “ 12 XY ”, where X and Y are positive integers. Find the probabilities that a) this four digit number is divisible by 3 ; b) this four digit number is divisible by 4 . 3. Tiffany, Sirica and Karen are students. They are asked to solve a Maths problem indepently. Given that the probability of solving the problem successfully of Tiffany, Sirica and Karen are 0.2 , 0.3 and 0.6 respectively. a) Find the probability that only Karen can solve the problem. b) Find the probability that Tiffany and Sirica can solve the problem only. c) Find the probability that at least two of them can solve the problem. 4. Box A contains 4 white balls and 2 black balls. Box B contains 2 white balls and 3 black balls. One ball is drawn from Box A and placed in Box B. a) What is the probability that the ball drawn from Box B is white? b) What is the probability that the ball drawn from Box B is different from that drawn in Box A. 5. A box contains 40 coins, it is given that 12 of them is $10 and others is $5 . Charlotte selects three coins randomly without replacement. What is the probability that the value of coins selects is more that $18 ? 6. Anthony is a primary six student. He takes part in an Mathematics exam. In the exam, there are 5 multiple choice questions and 4 choices in each question. The passing marks is more than or equal to three questions out of 5 are correct. a) Find the probability that Anthony passes the exam. After the exam, he goes back home either by bus or taxi. If he passes the exam, the probability of taking bus is three times that of taking taxi. But if he fails, the probability of taking bus is five times that of taking taxi. b) Find the probability that he will take a taxi. 7. Crystal has 8 gold coins and 2 silver coins. And Rachel has 6 gold coins and 4 silver coins. If they exchange one coin randomly, Find the probalility that the number of gold and silver coins of them is unchange. 8. There are 4 white balls and 6 black balls in a bag. Emily randomly selects a ball from the bag one by one without replacement until a white ball are selected. Find the probability that a) she selects the white ball in the first attempt; b) she selects the white ball at most three attempts. - Page 1-

HKDSE Exercise

MATHEMATICS (Core)

Answer

1 1 1 × = 5 5 25 3 2 12 × ×2= b) 5 5 25 34 17 = a) 100 50 25 1 = b) 100 4 a) 0.8×0.7×0.6=0.336 b) 0.2×0.3×0.4=0.024 c) 0.2×0.3×0.4+0.8×0.3×0.6+0.2×0.7×0.6+0.2×0.3×0.6=0.288 4 3 2 2 4 × + × = a) 6 6 6 6 9 4 3 2 2 4 × + × = b) 6 6 6 6 9 28×27×26 127 1− = 40×39×38 190 3 2 4 5 1 3 1 3 1 53 a) 10×( ) ×( ) +5×( ) ×( )+( ) = 4 4 4 4 4 512 1 359 512−53 1 359 × + × = b) 4 2048 512 6 2048 8 6 2 4 14 × + × = 10 10 10 10 25 4 2 = a) 10 5 2 6 4 6 5 4 5 + × + × × = b) 5 10 9 10 9 8 6

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By HENRY LEUNG