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
4 purple marbles
Question content area bottom
Part 1
  
enter your response here times
Round to the nearest whole number.

Answer 1

To predict the number of times you will pick a purple marble when selecting a marble at random and replacing it each time, first, determine the probability of selecting a purple marble.

You have:

- 5 blue marbles
- 4 purple marbles

In total, there are \(5 + 4 = 9\) marbles.

The probability of picking a purple marble on any individual draw is:

\[
P(\text{Purple}) = \frac{\text{Number of Purple Marbles}}{\text{Total Number of Marbles}} = \frac{4}{9}
\]

Now, if you are picking a marble 10 times, the expected number of times you will pick a purple marble can be calculated using the following formula:

\[
\text{Expected Number of Purple Marbles} = 10 \times P(\text{Purple}) = 10 \times \frac{4}{9}
\]

Calculating that value:

\[
10 \times \frac{4}{9} = \frac{40}{9} \approx 4.44
\]

Rounding to the nearest whole number, we get:

\[
\text{Expected Number of Purple Marbles} \approx 4
\]

Thus, the best prediction for the number of times you will pick a purple marble is **4 times**.