Question

question 5 (multiple choice worth 2 points) (experimental probability mc) there are 10 brown, 10 black, 10 green, and 10 gold marbles in bag. a student pulled a marble, recorded the color, and placed the marble back in the bag. the table below lists the frequency of each color pulled during the experiment after 40 trials. outcome frequency brown 13 black 9 green 7 gold 11 compare the theoretical probability and experimental probability of pulling a gold marble from the bag. the theoretical probability, p(gold), is 25%, and the experimental probability is 27.5%. the theoretical probability, p(gold), is 50%, and the experimental probability is 11.5%. the theoretical probability, p(gold), is 25%, and the experimental probability is 25%. the theoretical probability, p(gold), is 50%, and the experimental probability is 13.0%.

Explanation:

Step1: Calculate theoretical probability of gold

There are 4 colors of marbles with equal - number (10 of each color initially), so the theoretical probability of getting a gold marble, $P(\text{gold})=\frac{10}{10 + 10+10 + 10}=\frac{10}{40}=0.25 = 25\%$.

Step2: Calculate experimental probability of gold

The experimental probability is calculated by the formula $P=\frac{\text{number of favorable outcomes}}{\text{total number of outcomes}}$. The number of times a gold marble was pulled is 11, and the total number of trials is 40. So the experimental probability of getting a gold marble, $P(\text{gold})=\frac{11}{40}=0.275 = 27.5\%$.

Answer:

The theoretical probability, P(gold), is 25%, and the experimental probability is 27.5%