Question

According to Masterfoods, the company that manufactures M&M’s, 12% of peanut M&M’s are brown, 15% are yellow, 12% are red, 23% are blue, 23% are orange and 15% are green. (Round your answers to 4 decimal places where possible)

Compute the probability that a randomly selected peanut M&M is not yellow.
Compute the probability that a randomly selected peanut M&M is orange or yellow.
Compute the probability that three randomly selected peanut M&M's are all red.
If you randomly select two peanut M&M's, compute that probability that neither of them are red.
If you randomly select two peanut M&M's, compute that probability that at least one of them is red.

Answer 1

Explanation:

According to Masterfoods, the company that manufactures M&M’s, 12% of peanut M&M’s are brown, 15% are yellow, 12% are red, 23% are blue, 23% are orange and 15% are green.

Colour Brown Yellow Red Blue Orange Green total

Prob 0.12 0.15 0.12 0.23 0.23 0.15 1

The probability that a randomly selected peanut M&M is not yellow

=
`1-P(Yellow) = 0.85`

the probability that a randomly selected peanut M&M is orange or yellow.

=
`0.23+0.15=0.38`

the probability that three randomly selected peanut M&M's are all red.

=
`(0.12)^3 = 0.001728`

(assuming large number of peanuts and thus independent )

If you randomly select two peanut M&M's, compute that probability that neither of them are red.

=
`(1-0.12)^2\\= 0.7744`

If you randomly select two peanut M&M's, compute that probability that at least one of them is red

=
`1-P(both non red)\\= 1-0.88^2\\= 0.2256`