Question
A bag contains 16 blue marbles, 12 red marbles, and 12 green marbles. If Malik randomly draws a marble from the bag (and puts it back) 25 times, how many times should he expect to pull a blue marble?
Answers
GPT-4o mini
To find the expected number of times Malik will draw a blue marble, we first need to calculate the total number of marbles in the bag.
The bag contains:
- 16 blue marbles
- 12 red marbles
- 12 green marbles
Total number of marbles = 16 + 12 + 12 = 40 marbles.
Next, we calculate the probability of drawing a blue marble. The probability \( P(\text{Blue}) \) is given by the formula:
\[
P(\text{Blue}) = \frac{\text{Number of blue marbles}}{\text{Total number of marbles}} = \frac{16}{40} = \frac{2}{5}.
\]
Now, since Malik draws a marble 25 times, the expected number of times he will draw a blue marble can be calculated using the expected value formula:
\[
E(\text{Number of blue marbles drawn}) = \text{Number of draws} \times P(\text{Blue}) = 25 \times \frac{2}{5}.
\]
Calculating that gives:
\[
E(\text{Number of blue marbles drawn}) = 25 \times \frac{2}{5} = 25 \times 0.4 = 10.
\]
Thus, Malik should expect to pull a blue marble **10 times** on average.
The bag contains:
- 16 blue marbles
- 12 red marbles
- 12 green marbles
Total number of marbles = 16 + 12 + 12 = 40 marbles.
Next, we calculate the probability of drawing a blue marble. The probability \( P(\text{Blue}) \) is given by the formula:
\[
P(\text{Blue}) = \frac{\text{Number of blue marbles}}{\text{Total number of marbles}} = \frac{16}{40} = \frac{2}{5}.
\]
Now, since Malik draws a marble 25 times, the expected number of times he will draw a blue marble can be calculated using the expected value formula:
\[
E(\text{Number of blue marbles drawn}) = \text{Number of draws} \times P(\text{Blue}) = 25 \times \frac{2}{5}.
\]
Calculating that gives:
\[
E(\text{Number of blue marbles drawn}) = 25 \times \frac{2}{5} = 25 \times 0.4 = 10.
\]
Thus, Malik should expect to pull a blue marble **10 times** on average.