Question

A basketball player that shoots 80% from the free throw line attempts two free throws. The notation for conditional probability is P(made 2nd attempt|made 1st attempt) .

Which notation is the probability of the two events being not independent?




P(made 2nd attempt|made 1st attempt)=P(made 1st attempt)P(made 2nd attempt)

P(made 2nd attempt|made 1st attempt)=P(made 2nd attempt)


​ P(made 2nd attempt|made 1st attempt)=P(made 1st attempt and made 2nd attempt)P(made 1st attempt) ​

​ P(made 2nd attempt|made 1st attempt)=P(made 2nd attempt)P(made 1st attempt) ​

Answer 1

Answer: P(made 2nd attempt|made 1st attempt)=P(made 1st attempt and made 2nd attempt)P(made 1st attempt) ​

Explanation:

A basketball player that shoots 80% from the free throw line attempts two free throws.

Let Event A be made 1st attempt by basket player and Event B be made 2nd attempt by basket player. These events are dependent or not independent.

A dependent event is when one event impact the outcome of another event in a situation of probability .

Here A is given event which already occurred (made 1st attempt) and probability of getting B (made 2nd attempt) after Event A is given by

The conditional probability of Event B given Event A is P(B|A)=P(A and B)/P(A) or P(made 2nd attempt|made 1st attempt)=P(made 1st attempt and made 2nd attempt)P(made 1st attempt) ​ .

Answer 2

Option 3

Explanation:

Let A and B be two dependent events, then the probability of A given that B occurred is: P (A | B) = P (B and A) / P (B)

This means, that if event B occurred, then, the probability of occurrence A, is equal to the probability of occurrence B and A, between the probability of B

Entocnes, for this case the correct notation is:

P (made 2nd attempt | made 1st attempt) = P (made 1st attempt and made 2nd attempt) /P (made 1st attempt)

So the correct answer for this question is the third option