there are 2 bags. One bag contains 25 quarters and 10 nickels, the other has 20 quarters and 20 nickels. A bag is randomly chosen and a coin is randomly selected from it.

Question

a) what is the probability that the coin is a quarter?

b)what is the expected value of the selected coin?

Answer 1

25Q+10N 5/7 are quarters, about 71.4% quarters

20Q+20N half are quarters = exactly 50% quarters

pick a coin at random:

average 71.4 and 50 = (71.4+50)/2 = 121.4/2 = 60.7%

P(Q) =(1/2)(25/35) x+(1/2)(20/40) = (1/2)(5/7+1/2)

= 5/14+1/4

= 17/28= about 61% chance of getting a Quarter