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# INTRO TO PROBABILITY STA 4321

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This 1 page Class Notes was uploaded by Golden Bernhard on Friday September 18, 2015. The Class Notes belongs to STA 4321 at University of Florida taught by Brett Presnell in Fall. Since its upload, it has received 18 views. For similar materials see /class/206553/sta-4321-university-of-florida in Statistics at University of Florida.

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Date Created: 09/18/15

5 9 P 9 c 7 STA 4321 Mathematical Statistics 1 Additional Problems Ch 2 Instructions These problems will not be collected so you are free to discuss them and work together Some of them may also be done as examples in class Feller An Introduction to Probability Theory and Its Applications Vol 1 Each of the 50 states has two senators A committee of 50 senators is to be selected at random Let A Florida is represented on the committee B all states are represented on the committee Find PA and PB Feller An Introduction to Probability Theory and Its Applications Vol I At a bridge table the 52 cards are randomly divided into four hands of 13 cards each What is the probability that each of the four hands contains an ace Suppose that a test for an performance enhancing drug has a false positive rate77 of 4 and a false negative rate77 of 3 and that 1 of wif eball players use the drug A randomly selected player tests positive for the drug What is the probability that the player uses the drug How does your answer change if 10 of wif eball players use the drug Feller An Introduction to Probability Theory and Its Applications Vol I It is known that 5 men out of 100 and 25 women out of 10000 are colorblind A person is chosen at random and found to be colorblind What is the conditional probability that the person is a male Assume that males and females occur in equal numbers Similar to exercise 2137 in the 7th edition of Wackerly Mendenhall and Scheaffer Mathematical Statistics and Its Applications Ten urns each contain 10 balls The kth urn contains k black and 10 7 k white balls An urn is selected at random and a ball is selected at random from that urn Given that the ball selected is black what is the probability that it was taken from the kth urn Exercises 2119 and 2138 in the 7th edition of Wackerly Mendenhall and Scheaffer Mathematical Statistics and Its Applications Suppose that two balanced dice are tossed repeatedly and the sum of the two uppermost faces is determined on each toss a What is the probability that we obtain a sum of 4 before we obtain a sum of 7 b Following is a description of the game of craps A player rolls two dice and computes the total of the spots showing If the player s rst toss is a 7 or an 11 the player wins the game If the rst toss is a 2 3 or 12 the player loses the game If the player rolls anything else 4 5 6 8 9 or 10 on the rst toss that value becomes the player s point If the player does not win or lose on the rst toss he tosses the dice repeatedly until he obtains either his point or a 7 He wins if he tosses his point before tossing a 7 and loses if he tosses a 7 before his point What is the probability that the player wins a game of craps Feller An Introduction to Probability Theory and Its Applications Vol I Die A has four red and two white faces whereas die B has two red and four white faces A coin is ipped once If it falls heads the game continues by throwing die A alone if it falls tails die B is to be used a Show that the probability of red at any throw is 12 b If the rst two throws resulted in red what is the probability of red at the third throw c If red turns up at the rst it throws what is the probability that die A is being used

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