Question

Example #3 - In a bag of reese's pieces, there are 28 orange ones, 15 yellow ones, and 12 brown ones, for a total of 55 pieces.

c) if we select one at random, then put it back and mix them up well so that the selections are random, what is the probability that both the first and second ones are yellow?

d) If we select one and keep it and then select a second one, what is the probability that both of them are yellow?

Answer 1

Total = 28 + 15 + 12 = 55

Yellow ones = 15

c) This is with replacement probability. In this we are putting the first selection back into the bag so the number of pieces into bag is not changing.

P(both yellow) =

Hence, 9/121 is the answer of this one.

d) This is without replacement. In this we are not putting the first piece back into the bag so the number of pieces into bag will change to 54 when we select the second piece.

P(both yellow) =

Hence, 7/99 is the answer of this part.

In the second selection, total pieces = 54 and remaining yellow pieces = 14 because we already have 1 yellow piece in hand and we are not putting that back. That's why number of total and yellow pieces are changed.

Please comment if any doubt. Thank you.