A raffle is held in a club in which 10 of the 35 members who bought raffle ticke

Question

A raffle is held in a club in which 10 of the 35 members who bought raffle tickets are good friends with the club president. The club president draws two winners. (Round your answers to four decimal places.) (a) If the two winners are drawn with replacement, what is the probability that a friend of the president wins each time? 0816 (b) If the two winners are drawn without replacement, what is the probability that a friend of the president wins each time? 0756 (c) If the two winners are drawn with replacement, what is the probability that neither winner is a friend of the president? (d) If the two winners are drawn without replacement, what is the probability that neither winner is a friend of the president?

Explanation / Answer

P( friend of president win) = 10/35

P( friend of president does not win) = 25/35

a)

With replacement.

P( friend of president win each time) = 10 / 35 * 10 / 35

= 0.0816

b)

Without replacement

P( friend of President win each time) = 10/35 * 9/34

(9/34 comes because sample taken without replacement, that first winner does not involve in a sample while

picking second. so there one less sample left.)

= 0.0756

c)

With replacement

If selected winner is not friend of president then it comes from remaining 25 winners.

P(Niether winner is friend of president) = 25/35 * 25/35

= 0.5102

d)

Without replacement.

P(Niether winner is friend of president) = 25/35 * 24/34

= 0.5042

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