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) a. Compute the probability that a randomly selected peanut M&M is not green. 0.850 b. Compute the probability that a randomly selected peanut M&M is green or red. c. Compute the probability that two randomly selected peanut M&M’s are both red. d. If you randomly select two peanut M&M’s, compute that probability that neither of them are red e. If you randomly select two peanut M&M’s, compute that probability that at least one of them is red.

Answer 1

Complete question

The complete question is shown on the first uploaded image

Answer:

a

  $y' = 0.85$

b

 $P(J) = 0.27$

c

 $P(R) = 0.0144$

d

  $P(R') = 0.7744$

e

 $P(Q) =0.2256$

Step-by-step explanation:

From the question we are told that

   The proportion of M & M's that is  brown is  b =  0.12

   The proportion of M & M's that is  yellow  is  y =  0.15

    The proportion of M & M's that is  red  is  r =  0.12

    The proportion of M & M's that is  blue  is  b =  0.23

    The proportion of M & M's that is  orange  is  o =  0.23

    The proportion of M & M's that is  green  is  g =  0.15

Generally the probability that a random selected M&M is not yellow is  

         $y' = 1-y$

=>      $y' = 1-0.15$

=>      $y' = 0.85$

Generally the probability that a randomly selected peanut M&M isgreen or red is mathematically represented as

       $P(J) = g + r$

=>    $P(J) = 0.15 + 0.12$

=>    $P(J) = 0.27$

Generally the  probability that two randomly selected peanut M&M’s are both red is mathematically represented as

      $P(R) = r^2$

=>    $P(R) = 0.12^2$

=>    $P(R) = 0.0144$

Generally if two  two peanut M&M’s are selected the probability that neither of them are red is mathematically represented as

     $P(R') = (1 -r)^2$

=>  $P(R') = (1 - 0.12)^2$

=>   $P(R') = 0.7744$

Generally if two  two peanut M&M’s are selected the probability that at least one of them is red is mathematically represented as

        $P(Q) = 1- P(R')$

=>      $P(Q) = 1- 0.7744$

=>      $P(Q) =0.2256$