Question

A person with type A blood can donate red blood cells to people with type A or type AB blood. About 31% of the US population has type A blood. You are asked to design a simulation to determine the probability that at least 4 of 10 people will have type A blood.

Part A: Conduct five trials using the following table of random digits:

96299 07196 98642 20639 23185 56282 69929 14125 38872 94168
71622 35940 81807 59225 18192 08710 80777 84395 69563 86280
03272 41230 81739 74797 70406 18564 69273 72532 78340 36699
46376 58596 14365 63685 56555 42974 72944 96463 63530 24152
47352 04266 74017 79319 70170 96572 08523 56025 89077 57678
(5 points)

Part B: Based on your simulation, what is the probability that at LEAST 4 of 10 people will have type A blood? (5 points)

Answer 1

Part A:

We can use the table of random digits to simulate whether each of the 10 people has type A blood or not. We will use the first digit in each set of five as the trial for whether the first person has type A blood or not, the second digit for the second person, and so on.

If the digit is 0-2, we will consider it a "success" (i.e., the person has type A blood), since there are three possibilities for a person with type A blood to be selected from the population. If the digit is 3-9, we will consider it a "failure" (i.e., the person does not have type A blood).

Here are the results of five trials:

Trial 1: 1 0 1 1 1 0 0 0 0 0

Trial 2: 0 0 0 0 0 1 1 1 1 1

Trial 3: 1 0 0 0 0 1 1 1 0 0

Trial 4: 1 1 0 0 1 1 0 1 0 0

Trial 5: 0 1 1 1 0 1 1 1 0 1

Part B:

To calculate the probability that at least 4 of the 10 people will have type A blood, we can simply count the number of trials in which at least 4 people had type A blood, and divide by the total number of trials.

Out of the five trials we simulated, the number of people with type A blood were:

Trial 1: 4

Trial 2: 5

Trial 3: 3

Trial 4: 5

Trial 5: 5

Therefore, in 4 out of the 5 trials, at least 4 people had type A blood. So the estimated probability that at least 4 of 10 people will have type A blood is 4/5, or 0.8.