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You select a marble without looking and then put it back. If you do this $10$ times, what is the best prediction possible for the number of times you will pick a green marble? $\newline$ $\newline$ $\_\_\_\_$ times

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Full solution

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

10

times, what is the best prediction possible for the number of times you will pick a green marble?

\newline

\newline

\_\_\_\_

times

Determine Total Marbles: Step $1$ : Determine the total number of marbles and the number of green marbles. Assume there are $20$ marbles in total, with $5$ being green.
Calculate Probability: Step $2$ : Calculate the probability of picking a green marble. Probability $P$ = Number of green marbles / Total number of marbles = $\frac{5}{20}$ = $\frac{1}{4}$ .
Predict Green Marbles: Step $3$ : Predict the number of times you will pick a green marble in $10$ tries. Expected number $= \text{Probability of green marble} \times \text{Number of tries} = \frac{1}{4} \times 10 = 2.5$ . Since you can't pick half a marble, round to $3$ .

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