Question

George has a bowl of cards. He has 3 Black and 7 Red. He had a friend pick a card from the bowl 40 × and then put it back. Here are the results: Red 16 ×, Black 24 ×.

a. What is the theoretical probability of picking a Black card? Red card?
b. What is the experimental probability of picking a Black card? Red card?
c. How does each theoretical probability compare to each relative frequency?
d. Based on the theoretical probabilities, how many × should George expect to get a Black and Red card? How do they compare with his experimental results?

Answer 1

The theoretical probability of picking a Black card is 3/10 and the theoretical probability of picking a Red card is 7/10. The experimental probability of picking a Black card is 0.6 and the experimental probability of picking a Red card is 0.4. The theoretical probabilities are different from the relative frequencies obtained from the experiments.

Step-by-step explanation:

a. The theoretical probability of picking a Black card is 3/10 and the theoretical probability of picking a Red card is 7/10. This is because out of the total 10 cards, 3 are Black and 7 are Red.

b. The experimental probability of picking a Black card is 24/40 = 0.6 and the experimental probability of picking a Red card is 16/40 = 0.4. This is because out of the 40 trials, Black was picked 24 times and Red was picked 16 times.

c. The theoretical probabilities and relative frequencies are different because theoretical probabilities are based on mathematical calculations, while relative frequencies are based on actual experimental results.

d. Based on the theoretical probabilities, George should expect to get 4 Black cards and 6 Red cards out of 10 trials. The experimental results show that he got 24 Black cards and 16 Red cards out of 40 trials, which is close to the expected values.