Question

If you were to pull a random marble from the bag 100 times (putting the marble back each time and picking a new marble randomly), how many times out of 100 would you expect to pull a yellow marble? (Show work)

A. 0
B. 10
C. 25
D. 50

Answer 1

The probability of pulling a yellow marble in one draw from a bag containing 9 marbles (2 of which are yellow) is 2/9. Over 100 draws, you would expect to pull a yellow marble about 22 times (2/9 * 100).

Step-by-step explanation:

To determine how many times out of 100 you would expect to pull a yellow marble, you first need to calculate the probability of drawing a yellow marble in a single draw. You then multiply this probability by 100 to predict the outcome over 100 draws. The bag contains a total of 9 marbles (4 green, 3 red, and 2 yellow). So, the probability of drawing a yellow marble in one draw is the number of yellow marbles divided by the total number of marbles:

Probability of drawing a yellow marble = Number of yellow marbles ÷ Total number of marbles = 2 ÷ 9

For 100 draws, the expected number of times you would draw a yellow marble is:

Expected number of yellow marbles = Probability of yellow marble × 100 draws = (2 ÷ 9) × 100 ≈ 22.22

Since you can't draw a fraction of a marble, the closest estimate is that you would draw a yellow marble approximately 22 times out of 100 draws.