Question

NCAA stated that of the nearly 8,000,000 high school students participating in high school athletics, only 460,000 of those students will compete at an NCAA college. For the sport of baseball in particular, there are 482,629 high school players. Of these, 6.9% will play in an NCAA college and 8.6% of the college players will go on to be drafted by the MLB. What is the probability that a baseball player will play at an NCAA college and will also go on to be drafted by the MLB?

Answer 1

Answer:

0.5934% probability that a baseball player will play at an NCAA college and will also go on to be drafted by the MLB

Step-by-step explanation:

We use the conditional probability formula to solve this question. It is

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

In which

P(B|A) is the probability of event B happening, given that A happened.

$P(A \cap B)$ is the probability of both A and B happening.

P(A) is the probability of A happening.

In this question:

Event A: Playing at an NCAA college.

Event B: Being drafted by the MLB.

6.9% will play in an NCAA college

This means that $P(A) = 0.069$

8.6% of the college players will go on to be drafted by the MLB.

This means that $P(B|A) = 0.086$

What is the probability that a baseball player will play at an NCAA college and will also go on to be drafted by the MLB?

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

$P(A \cap B) = P(A) \times P(B|A)$

$P(A \cap B) = 0.069*0.086 = 0.005934$

0.5934% probability that a baseball player will play at an NCAA college and will also go on to be drafted by the MLB