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In: Statistics and Probability

According to Masterfoods, the company that manufactures M&Ms, 12% of peanut M&Ms are brown, 15% are...

According to Masterfoods, the company that manufactures M&Ms, 12% of peanut M&Ms are brown, 15% are yellow, 12% are red, 23% are blue, 23% are orange and 15% are green. Assume that selecting multiple M&Ms are independent events. (Round your answers to three decimal places, for example: 0.123)

Compute the probability that a randomly selected peanut M&M is not yellow.

A:

Compute the probability that four randomly selected peanut M&Ms are all yellow.

A:

If you randomly select five peanut M&Ms, compute that probability that none of them are red.

A:

Solutions

Expert Solution

Answer:

Given that,

According to Masterfoods,

The company that manufactures M&Ms, 12% of peanut M&Ms are brown, 15% are yellow, 12% are red, 23% are blue, 23% are orange and 15% are green.

Assume that selecting multiple M&Ms are independent events.

(a).

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

Given 15% are yellow,

The probability that a randomly selected peanut M&M is not yellow=P[Peanut is not yellow]

=1-0.15

=0.85

Therefore,  the probability that a randomly selected peanut M&M is not yellow is 0.85

(b).

The probability that four randomly selected peanut M&Ms are all yellow:

Given 15% are yellow,

The probability that four randomly selected peanut M&Ms are all yellow=P[ 4 randomly selected peanuts are yellow]

=0.150.150.150.15

=0.00051

=0.001( Approximately)

Therefore, the probability that four randomly selected peanut M&Ms are all yellow is 0.001.

(c).

The probability that none of them are red:

Given 12% are red.

If you randomly select five peanut M&Ms, that none of them red=P[ 5 randomly selected peanuts are not red]

=(1-0.12)(1-0.12)(1-0.12)(1-0.12)(1-0.12)

=(1-0.12)5

=(0.88)5

=0.5277

=0.528(Approximately)

Therefore, the probability is 0.528

orchestra answered 1 year ago
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