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You select a marble without looking and then put it back. If you do this $9$ times, what is the best prediction possible for the number of times you will pick an orange 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

9

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

\newline

\newline

_____ times

Determine Total Marbles: Step $1$ : Determine the total number of marbles and the number of orange marbles. Assume there are $20$ marbles in total, with $5$ being orange.
Calculate Probability: Step $2$ : Calculate the probability of picking an orange marble. Probability $P$ = Number of orange marbles / Total number of marbles = $\frac{5}{20}$ = $\frac{1}{4}$ .
Predict Marble Picks: Step $3$ : Use the probability to predict the number of times an orange marble will be picked in $9$ trials. Expected number of times = Probability of picking an orange marble $\times$ Number of trials = $\frac{1}{4} \times 9 = 2.25$ . Since we can't pick a fraction of a marble, round down to $2$ .

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