3. -10 points My Notes Ask Your Teacher . The governor and lieutenant governor f

Question

3. -10 points My Notes Ask Your Teacher . The governor and lieutenant governor from 7 states are attending a workshop. Two identical door prizes are randomly awarded to two different attendees. Answer the following questions. (Give your answers correct to three decimal places.) (a) What is the probability one prize goes to a governor and one to a lieutenant governor? (b) What is the probability that both prizes go to officials from the same state? (c) Gov. Susan Canup and Lt. Gov. Robert Lufkin are the officials from Illinois attending the workshop. If Lt. Gov. Lufkin wins a prize, what is the conditional probability that Gov. Canup will win the other prize? d) If Lt. Gov. Corker does not win a prize, then what is the conditional probability that Gov. Crump will win one of the two prizes?

Explanation / Answer

Solution :

Given ,

total number of officials attending the workshop = 14( includes the governer and the lieutnent governoes of each state)

number of door prizes = 2

( a )

the probability that one prize goes to a governor and one to a lieutnent governor =( 7c1 * 7c1) / 14c2

= 49 / 91

= 0.5384

( b )

probability that both prizes go to same state = 7 / 91 = 0.0769

( c )

given Gov. lufkin wins a prize ,the probability that Gov. Canup wins the other prize = 1 / 13 = 0.0769

( d )

given Gov.Corker does not win a prize,the probability that Gov.Crump winning one of the two prizes

= 12 / 13c2 = 0.1538

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