STAT 400 Lecture AL1 Practice Problems 1 Spring 2015 Dalpiaz 1 A statistics instructor teaches two statistics classes back to back lecture AL1 at 11 00 am and lecture CL1 at 12 noon Suppose the probability that the instructor gives a good AL1 lecture is 0 25 If AL1 lecture is good then CL1 lecture is also good with probability 0 50 However if AL1 lecture is bad then there is an 90 chance that CL1 lecture will also be bad a What proportion of the CL1 lectures are good b Suppose CL1 lecture was good What is the probability that AL1 lecture was also good c If at the conclusion of the CL1 lecture the instructor is heard to mutter what a rotten lecture what is the probability that the AL1 lecture was also bad d What is the probability that at least one lecture is good i e either AL1 lecture is good or CL1 lecture is good or both 2 1 3 4 c 1 4 4 c Two cards are drawn successively and without replacement from an ordinary deck of playing cards Compute the probability of drawing a heart on the first draw and an ace on the second draw Hint Note that a heart can be drawn by getting the ace of hearts or one of the other 12 hearts 3 Bowl A contains three red and two white chips and bowl B contains four red and three white chips A chip is drawn at random from bowl A and transferred to bowl B a 1 3 16 1 4 18 Compute the probability of then drawing a red chip from bowl B b If a red chip was drawn from bowl B what is the probability that a red chip had been drawn from bowl A 4 Consider two events A and B such that P A 0 70 P B 0 40 and P A B 0 82 Are A and B independent 5 At a hospital s emergency room patients are classified and 20 of them are critical 30 are serious and 50 are stable Of the critical ones 30 die of the serious 10 die and of the stable 2 die a 1 5 5 1 6 5 Given that a patient dies what is the conditional probability that the patient was classified as critical As serious As stable b Are events a patient dies and a patient was classified as critical independent Justify your answer c Are events a patient dies and a patient was classified as serious independent Justify your answer 6 Does a monkey have a better chance of rearranging ACCLLSUU to spell CALCULUS or AABEGLR 7 to spell ALGEBRA Three cards are drawn at random without replacement from a standard 52 card deck What is the probability that either all three cards are face cards king queen jack or all three cards are red cards or both 8 A laboratory has 15 rats 7 white 6 gray and 2 brown Suppose 5 rats will be selected at random and assigned to an experimental drug a Find the probability that 2 white 2 gray and 1 brown rats were selected b Find the probability that 3 white and 2 gray rats were selected c Find the probability that all five rats selected have the same color d Find the probability that all five rats selected have different color 9 A bank has two emergency sources of power for its computers There is a 95 chance that source 1 will operate during a total power failure and an 80 chance that source 2 will operate Assume the power sources are independent What is the probability that at least one of them will operate during a total power failure 10 If a fair 6 sided die is rolled 6 times what is the probability that each possible outcome 1 2 3 4 5 and 6 will occur exactly once 11 1 3 7 1 4 9 An urn contains four colored balls two orange and two blue Two balls are selected at random without replacement and you are told that at least one of them is orange What is the probability that the other ball is also orange Hint 1 OO OB BO Hint 2 P both orange at least one orange BB 12 A new flavor of toothpaste has been developed It was tested by a group of 15 people Nine of the group said they liked the new flavor and the remaining 6 indicated they did not Five of the 15 are selected at random to participate in an in depth interview a What is the probability that of those selected for the in depth interview 4 liked the new flavor and 1 did not b What is the probability that of those selected for the in depth interview at least 4 liked the new flavor 13 A company that manufactures video cameras produces a basic model and a deluxe model Suppose that 25 of the cameras sold are the basic model Of those buying the basic model 20 purchase an extended warranty whereas 40 of the deluxe model purchasers do so a What proportion of customers purchase an extended warranty b What proportion of customers either purchase an extended warranty or purchase a deluxe model or both c If you learn that a randomly selected purchaser has an extended warranty what is the probability that he she has a deluxe model d Suppose a randomly selected purchaser does not have an extended warranty What is the probability that he she has a basic model 1 A statistics instructor teaches two statistics classes back to back lecture AL1 at 11 00 am and lecture CL1 at 12 noon Suppose the probability that the instructor gives a good AL1 lecture is 0 25 If AL1 lecture is good then CL1 lecture is also good with probability 0 50 However if AL1 lecture is bad then there is an 90 chance that CL1 lecture will also be bad A good AL1 lecture C good CL1 lecture a P C A 0 90 P C A 0 50 P A 0 25 What proportion of the CL1 lectures are good P C P A C P A C P A P C A P A P C A 0 25 0 50 0 75 0 10 0 125 0 075 0 20 OR b C C Total A 0 25 0 50 0 125 0 125 0 25 A 0 075 0 75 0 90 0 675 0 75 Total 0 20 0 80 1 00 Suppose CL1 lecture was good What is the probability that AL1 lecture was also good P A C P A C 0 125 5 0 625 P C 0 20 8 OR P A C P A P C A P A P C A P A P C A 0 25 0 50 0 125 5 0 25 0 50 0 75 0 10 0 20 8 c If at the conclusion of the CL1 lecture the instructor is heard to mutter what a rotten lecture what is the probability that the AL1 lecture …
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