Question

A bag has 5 yellow marbles, 3 red marbles, and 2 blue marbles. Quinn randomly picks a marble from the bag and returns it before another is picked.



How many times would Quinn expect to pick a blue marble if he picks a marble 200 times?

Answer options with 5 options
A.
20

B.
40

C.
50

D.
60

E.
100

Answer 1

To determine how many times Quinn would expect to pick a blue marble when he picks a marble 200 times, we first need to calculate the probability of picking a blue marble in one draw.

There are:
- 5 yellow marbles
- 3 red marbles
- 2 blue marbles

This gives a total of:
\[
5 + 3 + 2 = 10 \text{ marbles}
\]

The probability \( P \) of picking a blue marble in one draw is:
\[
P(\text{blue}) = \frac{\text{Number of blue marbles}}{\text{Total number of marbles}} = \frac{2}{10} = \frac{1}{5}
\]

Next, to find the expected number of blue marbles picked in 200 draws, we multiply the total number of draws by the probability of picking a blue marble:
\[
\text{Expected number of blue marbles} = 200 \times P(\text{blue}) = 200 \times \frac{1}{5} = 40
\]

Therefore, the expected number of times Quinn would pick a blue marble if he picks a marble 200 times is:

**B. 40**