Question

M&M Probabilities

In 2002, the US voted for a new M&M color.  The results were 42% purple, 37% teal, and 19% pink.  When expressed as probabilities, these numbers are 0.42, 0.37, and 0.19, respectively.  Use the probabilities when performing calculations.  Give all answers to 4 decimal places.

1. What is the probability that a respondent selected at random preferred purple or pink? (1 pts.)

2. What is the probability that a respondent selected at random did not choose pink? (1 pts.)

3. If we pick two respondents at random, what is the probability that both choose teal? (2 pts.)

4. If we pick four respondents at random, what is the probability that none of those four choose teal? (2 pts.)

5. If we pick two respondents at random, what is the probability that the first person picks teal and the second person picks pink? (2 pts.)

6. If we pick ten respondents at random, what is the probability that at least one preferred purple?

Answer 1

P(purple) = 0.42, P(teal) = 0.37, P(pink) = 0.19

(a)

Ans = P(purple) + P(pink) = 0.42 + 0.19 = 0.61

(b)

Ans = P(pink') = 1 - P(pink) = 1-0.19 = 0.81

(c)

Ans = P(teal) * P(teal) = 0.37 * 0.37 = 0.1369

(d)

P(teal') = 1 - P(teal) = 1 - 0.37 = 0.63

(e)

Ans = P(teal) * P(pink) = 0.37 * 0.19 = 0.0703

(f)

If we pick ten respondents at random, what is the probability that no one preferred purple, = (1 - P(purple))¹⁰ = 0.58¹⁰

So, If we pick ten respondents at random, what is the probability that at least one preferred purple = 1 - 0.58¹⁰ = 0.99569

** If the answers do not match or any kind of confusion please comment