A bag contains 2 blue marbles, 2 red marbles, and 2 yellow marbles.If Jenna randomly draws a marble from the bag (and puts it back) 15 times, how many times should she expect to pull a yellow marble?

1 answer

To determine how many times Jenna should expect to pull a yellow marble after drawing a marble 15 times, we first need to find the probability of drawing a yellow marble in one draw.

Jenna's bag contains:

  • 2 blue marbles
  • 2 red marbles
  • 2 yellow marbles

In total, there are \( 2 + 2 + 2 = 6 \) marbles in the bag.

The probability \( P \) of drawing a yellow marble in one draw is given by the formula:

\[ P(\text{yellow}) = \frac{\text{number of yellow marbles}}{\text{total number of marbles}} = \frac{2}{6} = \frac{1}{3} \]

Now, if Jenna draws a marble 15 times, the expected number of times she will pull a yellow marble can be calculated using the formula for the expected value:

\[ \text{Expected value} = \text{number of trials} \times P(\text{yellow}) \]

Substituting the values we have:

\[ \text{Expected value} = 15 \times \frac{1}{3} = 5 \]

Therefore, Jenna should expect to pull a yellow marble \( \boxed{5} \) times.