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

Answer: 0.068

Step-by-step explanation:

Let we denote event A for choosing a left-handed player and event B for choosing a baseball player.

Given : The probability that a randomly chosen person is a left-handed baseball player : $P(A\cap B)=0.017$

The conditional probability that a randomly chosen baseball player is left-handed :

$P(A|B)=0.250$

Using the formula for conditional probability:-

$P(A|B)=\dfrac{P(A\cap B)}{P(B)}\\\\\Rightarrow\ P(B)=\dfrac{P(A\cap B)}{P(A|B)}$

i.e. the  probability, , that a randomly chosen person from this country plays baseball will be :

$P(B)=\dfrac{0.017}{0.250}=0.068$

Hence, the required probability : 0.068