Question

Another bag contains 8 black counters and 12 white counters. One counter is taken out of the bag and then returned. This is done 50 times and the color is noted.

Black- 18
White- 32

a. Use the results of the 50 experiments to estimate the probability of a black counter
being picked from the bag. Simplify your answer fully.
b. What is the theoretical probability of a black counter being picked from the bag?
Simplify your answer fully.
c. If the experiment was repeated 200 times, how often would you expect a white
counter to be chosen?

Answer 1

Answer below.

Step-by-step explanation:

A. The estimated probability of drawing a black counter can be calculated as the ratio of the number of times a black counter was chosen to the total number of experiments:

Estimated probability of black counter = Number of black counters chosen / Total number of experiments = 18/50 = 9/25.

B. The theoretical probability of drawing a black counter can be calculated as the ratio of the number of black counters in the bag to the total number of counters in the bag:

Theoretical probability of black counter = Number of black counters / Total number of counters = 8/(8+12) = 2/5.

C. If the experiment were repeated 200 times, we would expect to draw a white counter on approximately (32/50)*200 = 128 occasions. This can be calculated as follows: the estimated probability of drawing a white counter from the first 50 experiments is 32/50. Multiplying this by the total number of experiments (200) gives the expected number of times a white counter will be chosen.