Question

Suppose there are 6 runners in the finals of a 100 m sprint, Abbie, Becca, Clarice, Danna, Emma, and Francine. Answer each of the following questions.

1. An analyst, Grace, gives Abbie a 12% chance to place first and Becca an 8% chance to place second. Assume these percentages are accurate. Can we determine the probability that Abbie will place first and Becca will place second? Why or why not?

Answer 1

No, the events are dependent

Explanation:

The probability of two events occurring is:

P(A and B) = P(A) × P(B given A)

If the events are independent (event A does not affect the probability of event B), then P(B given A) = P(B).

However, these events aren't independent. If Abbie places first, it affects the probability of whether Becca places second.

P(B given A) ≠ P(B)

P(B given A) ≠ 0.08