Question

A. A party mix of candy contains a blend of M&Ms, Reese's Pieces, and Skittles. The blend is 50% M&Ms, 30% Reese's Pieces, and 20% Skittles. M&Ms are 14% yellow, Reese's Pieces are 25% yellow, and Skittles are 20% yellow.
Express all probabilities as decimals, rounded to four places.

1. If you pull a yellow piece of candy from the mix, what is the probability it is an M&M?

2.  If you pull a non-yellow piece of candy from the mix, what is the probability it is an M&M?

3. If you pull a piece of candy other than an M&M from the mix, what is the probability it is yellow?

Answer 1

(a) P(Yellow) = P(M&M & yellow) + P(Reese & yellow) + P(Skittles & yellow)

P(Yellow) = (0.50 * 0.14) + (0.30 * 0.25) + (0.20* 0.20)

P(Yellow)= 0.1850

(b) P( M&M / non yellow) = P( M&M and non yellow) / P(non yellow)  

P(non yellow & M&M) = 0.50 * 0.86 = 0.4300

P(non yellow) = 1 - 0.1850 = 0.8150

P( M&M / non yellow) = 0.4300 / 0.8150 = 0.5276

P( M&M / non yellow) = 0.5276

(c) P( yellow / other than M&M) = P( yellow and non M&M) / P(non M&M)  

  P( yellow / other than M&M) = (0.0750+ 0.0400)  / 0.50 = 0.1150 / 0.50

P( yellow / other than M&M) = 0.2300