Question

4.2 theoretical probability. mutually exclusive/not mutually exclusive. the number of m&ms of each color that were found in a case with m&ms is given in the table below: color freq blue 367 brown 317 green 449 orange 354 red 135 yellow 416 a) find the probability that a randomly selected m&m will be in the category \orange\ or
ed\. give your answer as a fraction. give your answer rounded to three decimal places. b) find the probability that a randomly selected m&m is not in the category \orange\. given your answer as a fraction. give your answer rounded to three decimal places. question help: video 1 video 2 message instructor submit question

Explanation:

Step1: Calculate total number of M&Ms

$367 + 317+449 + 354+135+416=2038$

Step2: Calculate probability for part a (fraction)

Number of orange or red M&Ms is $354 + 135=489$. Probability as a fraction is $\frac{489}{2038}$.

Step3: Calculate probability for part a (decimal)

$\frac{489}{2038}\approx0.239$

Step4: Calculate probability for part b (fraction)

Number of non - orange M&Ms is $2038-354 = 1684$. Probability as a fraction is $\frac{1684}{2038}=\frac{842}{1019}$.

Step5: Calculate probability for part b (decimal)

$\frac{1684}{2038}\approx0.826$

Answer:

a) $\frac{489}{2038}$, $0.239$
b) $\frac{842}{1019}$, $0.826$