If you draw an M&M; candy at random from a bag of the candies, the candy you dra

Question

If you draw an M&M; candy at random from a bag of the candies, the candy you draw will have one of six colors. The probability of drawing each color depends on the proportion of each color among all candies made (a) The table below gives the probability of each color for a randomly chosen plain M&. Color:Bown Red Yellow Green Orange Blue Probability: 0. 2 0.1 0.1 0. What must be the probability for drawing a blue candy? (b) The probabilities for peanut M&Ms; are a bit different. Color:Brown Red Yellow Gren Orange Blue Probability: 0.1 0.1 0.1 0.1 0.1 ? What is the probability that a peanut M&M; chose at randomis blue? c) What is the probability that a plain M&M; is any of red, yellow, or orange? What is the probability that a peanut M&M; has one of these colors?

Explanation / Answer

(a) Sum of the probabilities must be 1

=> 0.1 + 0.2 + 0.1 + 0.1 + 0.1 + P(blue) = 1

=> 0.6 + P(blue) = 1

=> P(blue) = 1 - 0.6 = 0.4.

(b) 0.1 + 0.1 + 0.1 + 0.1 + 0.1 + P(blue) = 1

=> 0.5 + P(blue) = 1

=> P(blue) = 1 - 0.5 = 0.5.

(c) Probability that a plain M&M is any of red, yellow or orange

= 0.2 + 0.1 + 0.1

= 0.4.

Probability that a peanut M&M is any of red, yellow or orange

= 0.1 + 0.1 + 0.1

= 0.3.

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