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 302 brown 154 green 153 orange 486 red 188 yellow 422 a) find the probability that a randomly selected m&m will be in the category
ed\ or \green\. 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
ed\. given your answer as a fraction. give your answer rounded to three decimal places. question help: video 1 video 2 message instructor

Explanation:

Step1: Calculate total number of M&Ms

$302 + 154+153 + 486+188+422=1705$

Step2: Calculate probability for part a (fraction)

The number of red or green M&Ms is $188 + 153=341$. The probability $P(\text{red or green})=\frac{188 + 153}{1705}=\frac{341}{1705}$

Step3: Calculate probability for part a (decimal)

$P(\text{red or green})=\frac{341}{1705}\approx 0.200$

Step4: Calculate probability for part b (fraction)

The number of non - red M&Ms is $1705-188 = 1517$. The probability $P(\text{not red})=\frac{1705 - 188}{1705}=\frac{1517}{1705}$

Step5: Calculate probability for part b (decimal)

$P(\text{not red})=\frac{1517}{1705}\approx0.890$

Answer:

a) $\frac{341}{1705}$, $0.200$
b) $\frac{1517}{1705}$, $0.890$