Colors of M&M's candies. When first produced in 1940, M&M's Plain Chocolate Candies came in only brown color. Today, M&Ms in standard bags come in six colors: brown, yellow, red, blue, orange, and green. According to Mars Corporation, 24% of all M&Ms produced are blue, 20% are orange, 16% are green, 14% are yellow, 13% are brown, and 13% are red. Suppose you purchase a randomly selected bag of M&M's Plain Chocolate Candies and randomly select one of the M&M's from the bag. The color of the selected M&M is of interest.

a. Identify the outcomes (sample points) of this experiment.

b. Assign reasonable probabilities to the outcomes, part a.

c. What is the probability that the selected M&M is brown (the original color)?

d. In 1960, the colors red, green, and yellow were added to brown M&Ms. What is the probability that the selected M&M is either red, green, or yellow?

e. In 1995, based on voting by American consumers, the color blue was added to the M&M mix. What is the probability that the selected M&M is not blue?

The sample and the method for assigning probabilities comprise a probability model. Sample space and sample point are two terms that are used interchangeably. A statistical experiment's sample space S is the set of all possible outcomes. A sample point is an outcome in a sample space. It is sometimes referred to as a sample space element or a sample space member.

Sample points:

1. Probability of selecting Blue.
2. Probability of selecting Orange.
3. Probability of selecting Green.
4. Probability of selecting Yellow.
5. Probability of selecting Brown.
6. Probability of selecting Red.

Hence, the sample points of this experiment are

$\mathbf{Outcomes}\mathbf{=}\mathbf{\{}\mathbf{blue}\mathbf{,}\mathbf{orange}\mathbf{,}\mathbf{green}\mathbf{,}\mathbf{yellow}\mathbf{,}\mathbf{brown}\mathbf{,}\mathbf{red}\mathbf{\}}\mathbf{.}$

$\begin{array}{c}\mathbf{P}\mathbf{\left(}\mathbf{blue}\mathbf{\right)}\mathbf{=}\mathbf{24}\mathbf{\%}\\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\frac{\mathbf{24}}{\mathbf{100}}\\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\mathbf{0}\mathbf{.}\mathbf{24}\end{array}$

$\begin{array}{c}\mathbf{P}\mathbf{\left(}\mathbf{orange}\mathbf{\right)}\mathbf{=}\mathbf{20}\mathbf{\%}\\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\frac{\mathbf{20}}{\mathbf{100}}\\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\mathbf{0}\mathbf{.}\mathbf{20}\end{array}$

$\begin{array}{c}\mathbf{P}\mathbf{\left(}\mathbf{green}\mathbf{\right)}\mathbf{=}\mathbf{16}\mathbf{\%}\\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\frac{\mathbf{16}}{\mathbf{100}}\\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\mathbf{0}\mathbf{.}\mathbf{16}\end{array}$

$\begin{array}{c}\mathbf{P}\mathbf{\left(}\mathbf{yellow}\mathbf{\right)}\mathbf{=}\mathbf{14}\mathbf{\%}\\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\frac{\mathbf{14}}{\mathbf{100}}\\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\mathbf{0}\mathbf{.}\mathbf{14}\end{array}$

$\begin{array}{c}\mathbf{P}\mathbf{\left(}\mathbf{brown}\mathbf{\right)}\mathbf{=}\mathbf{13}\mathbf{\%}\\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\frac{\mathbf{13}}{\mathbf{100}}\\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\mathbf{0}\mathbf{.}\mathbf{13}\end{array}$

$\begin{array}{c}\mathbf{P}\mathbf{\left(}\mathbf{red}\mathbf{\right)}\mathbf{=}\mathbf{13}\mathbf{\%}\\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\frac{\mathbf{13}}{\mathbf{100}}\\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\mathbf{0}\mathbf{.}\mathbf{13}\end{array}$

Hence, the probability to the outcomesP(blue)=0.24, P(orange)=0.20, P(green)=0.16, P(yellow)=0.14, P(brown)=0.13, P(red)=0.13.

$\begin{array}{c}\mathbf{P}\mathbf{\left(}\mathbf{brown}\mathbf{\right)}\mathbf{=}\mathbf{13}\mathbf{\%}\\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\frac{\mathbf{13}}{\mathbf{100}}\\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\mathbf{0}\mathbf{.}\mathbf{13}\end{array}$

Hence, the probability of Brown is0.13.

$$\begin{gathered} \mathbf{P}\mathbf{=}\mathbf{P}\mathbf{\left(}\mathbf{red}\mathbf{\right)}\mathbf{+}\mathbf{P}\mathbf{\left(}\mathbf{green}\mathbf{\right)}\mathbf{+}\mathbf{P}\mathbf{\left(}\mathbf{yellow}\mathbf{\right)} \\ \mathbf{}\mathbf{}\mathbf{=}\mathbf{0}\mathbf{.}\mathbf{13}\mathbf{+}\mathbf{0}\mathbf{.}\mathbf{16}\mathbf{+}\mathbf{0}\mathbf{.}\mathbf{14} \\ \mathbf{}\mathbf{}\mathbf{=}\mathbf{0}\mathbf{.}\mathbf{43} \end{gathered}$$

Hence, the probability of red, green, or Yellow is0.43.

$$\begin{gathered} \mathbf{P}\mathbf{\left(}\mathbf{notblue}\mathbf{\right)}\mathbf{=}\mathbf{1}\mathbf{-}\mathbf{P}\mathbf{\left(}\mathbf{blue}\mathbf{\right)} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\mathbf{1}\mathbf{-}\mathbf{0}\mathbf{.}\mathbf{24} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\mathbf{0}\mathbf{.}\mathbf{76} \end{gathered}$$

Hence, the probability of not being blue is0.76.