Lesson Plan Probability

PROBABILITY  LESSON PLAN

 Binomial Distribution Ten coins are thrown simultaneously. Find Find the probability of getting at least seven heads. 1. Ten

ga me in which their chances of winning are in the ratio 3:2. Find A’s A’s chance of winning 2. A and B plays a game at least three games out of five games played. 3. A coffee connoisseur claims that he can distinguish between a cup of instant coffee and a cup of   percolator coffee !" of the time. #t is agreed agre ed that his claim will be accepted if he correctly correctl y identifies at least ! of the $ cups. Find his chance of having the claim %i& accepted' %ii& re(ected' when he does have the ability he claims. 4. A multiple choice test consists of ) *uestions with 3 answers to each *uestion %of which only one is correct&. A student answers each *uestions by rolling a die and chec+ing the first answer if he gets , or  2' the second answer if he gets 3 or - and the third answer if he gets ! or $. To get a distinction' the student must secure at least !" correct answer. #f there is no negative mar+ing' what is the probability that the student secures a distinction 5. An irregular si/0faced die is thrown and the e/pectation that in the ,1 throws it will give five even numbers is twice the e/pectation that it will give four even numbers. ow many items in ,1'111 sets of  ,1 throws each' would you e/pect it to give not an even numbers 6. A department in a wor+s has ,1 machines which ma y need ad(ustment from time to time during the day. Three of these machines are old each having a probability of ,4,, of needing ad(ustment during the day' and  are new' having corresponding probabilities of ,42,. Assuming that no machine needs ad(ustment twice on the same day' determine the probabilities that on a particular day' da y' 5ust 2 old and no new machines need ad(ustment. (i) (ii) #f (ust 2 machines need ad(ustment' they are of the same type. 7. The probability of a man hitting a target is 6. #f he fires  times' what is the probability of his hitting the target at least twice (i) ow many times he fires so that the probability of his hitting at least once is greater than 243 (ii) 8. #n a precision bombing attac+ there is a !1" chance that any one bomb will stri+e the target. Two direct hits are re*uired to destroy the target completely. ow many bombs must be dropped to give a 77" chance or better of completely destroying the target 9. #n a binomial distribution consisting of ! independent trials' probabilities of , and 2 successes are 1.-17$ and 1.21-) respectively. Find the parameter 8p’ of the distribution. 10. 9ith the usual notations' find 8p’ for the binomial variate ' if n;$ and 7