Question

1. A bowl contains 9 M&Ms identical in every respect except color. There are 6 brown M&Ms, 1 blue M&M, and 2 yellow M&Ms. You draw one M&M from the bowl, note its color, and then eat it before drawing the second M&M and noting its color. .

A. Find the probability of drawing two M&Ms and getting at least one brown M&M.

B. Find the probability of drawing two M&Ms and getting two M&Ms of different colors.

Answer 1

Given

Total number of M&Ms = 9

Number of brown M&Ms = 6

Number of blue M&Ms = 1

Number of yellow M&Ms = 2

This is the problem of  drawing two M&Ms without replacement.

A)

Getting at least one brown M&M means getting one brown M&M or two brown M&M

i) for getting one brown M&M

Probability of getting one M&M = (6/9 * 3/8) + (3/9 * 6/8) = 1/2

ii) For getting two brown M&M

Probability of getting two M&M = 6/9 * 5/8 = 5/12

Therefore,the probability of drawing two M&Ms and getting at least one brown M&M = 1/2 + 5/12 = 0.9167

B)

Getting two M&Ms of different colors comprises of three cases :

i ) Getting one brown M&M and one blue M&M

Probability of getting one brown M&M and one blue M&M = ( 6/9 *1/8) + ( 1/9 * 6/8) = 1/6

ii) Getting one brown M&M and one yellow M&M

Probability of getting one brown M&M and one yellow M&M = (6/9 *2/8) +(2/9 * 6/8) = 1/3

iii) Getting one blue M&M and one yellow M&M

Probability of getting one blue M&M and one yellow M&M = (1/9 * 2/8) +( 2/9 *1/8) = 1/18

Now

the probability of drawing two M&Ms and getting two M&Ms of different colors = 1/6 + 1/3 + 1/18 = 0.5556