Question

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 purple​ marble?
5 blue marbles
9 purple marbles
Question content area bottom
Part 1
  
enter your response here times
Round to the nearest whole number.

Answer 1

To determine the best prediction for the number of times you will pick a purple marble when randomly selecting from a mixture of 5 blue marbles and 9 purple marbles, we first need to calculate the total number of marbles and the proportion of purple marbles.

1. **Total number of marbles**:
\[
5 \text{ (blue)} + 9 \text{ (purple)} = 14 \text{ (total marbles)}
\]

2. **Probability of picking a purple marble**:
\[
P(\text{purple}) = \frac{\text{Number of purple marbles}}{\text{Total number of marbles}} = \frac{9}{14}
\]

3. **Expected number of times to pick a purple marble in 10 trials**:
\[
\text{Expected number of purple marbles} = 10 \times P(\text{purple}) = 10 \times \frac{9}{14}
\]

Calculating that:
\[
\text{Expected number} = 10 \times \frac{9}{14} = \frac{90}{14} \approx 6.42857
\]

4. **Rounding to the nearest whole number**:
\[
\text{Rounded expected number} \approx 6
\]

So the best prediction for the number of times you will pick a purple marble in 10 selections is **6 times**.