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You select a marble without looking and then put it back. If you do this $8$ times, what is the best prediction possible for the number of times you will pick a marble that is not pink? $\newline$ Choices: $\newline$ (A) $6$ $\newline$ (B) $1$ $\newline$ (C) $5$ $\newline$ (D) $4$

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Full solution

Q. You select a marble without looking and then put it back. If you do this

8

times, what is the best prediction possible for the number of times you will pick a marble that is not pink?

\newline

Choices:

\newline

(A)

6

\newline

(B)

1

\newline

(C)

5

\newline

(D)

4

Total Marbles and Pink Count: First, we need to know the total number of marbles and how many of them are not pink. Let's assume there are $10$ marbles in total, and $2$ of them are pink. This means $8$ marbles are not pink.
Calculate Probability of Non-Pink Marble: Next, we calculate the probability of picking a non-pink marble in one draw. Probability = Number of non-pink marbles / Total number of marbles = $\frac{8}{10} = 0.8$ .
Expected Number of Non-Pink Marbles: Since the event of picking a marble is repeated $8$ times with replacement, we multiply the probability of picking a non-pink marble by the number of trials. Expected number of times picking non-pink marble = $0.8 \times 8 = 6.4$ . Since we can't pick a fraction of a marble, we round down to $6$ .

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