Question

Suppose that in a particular country, the probability that a randomly chosen person is a left-handed baseball player is 0.017 and the probability that a randomly chosen baseball player is left-handed is 0.250. Based on these probabilities, determine the probability, , that a randomly chosen person from this country plays baseball. Give your answer as a decimal precise to at least three decimal places.

Answer 1

To determine the probability that a randomly chosen person from this country plays baseball, we can use the formula for conditional probability.

Step-by-step explanation:

To determine the probability that a randomly chosen person from this country plays baseball, we can use the formula for conditional probability.

Let A represent the event that a person plays baseball, and B represent the event that a person is left-handed. We are given that P(B) = 0.017 (the probability that a randomly chosen person is left-handed) and P(B|A) = 0.250 (the probability that a randomly chosen baseball player is left-handed).

To find P(A), we can use the formula P(A) = P(A|B) * P(B) + P(A|B') * P(B'), where B' represents the complement of event B. Since being left-handed is independent of playing baseball, P(A|B) = P(A|B') = P(A). Let's calculate the probability:

P(A) = P(A|B) * P(B) + P(A|B') * P(B') = P(A) * P(B) + P(A) * (1-P(B))

0.017 = P(A) * 0.017 + P(A) * (1-0.017)

0.017 = 0.017 * P(A) + 0.983 * P(A)

0.017 = P(A) * (0.017 + 0.983)

0.017 = P(A) * 1.000

P(A) = 0.017 / 1.000 = 0.017

Therefore, the probability that a randomly chosen person from this country plays baseball is 0.017, or 1.7%.