Question

Question 3 (1 point)

At the beginning of the basketball season, the coach noticed that for a randomly selected shot at the basket, the probability that the ball hits

the rim whether it goes in or not is 0.19. the probability that the shot is made whether it hits the rim or not is 0.17, and the probability that the

ball hits the rim and goes in is 0.05. Find the probability that a randomly selected shot either hits the rim or goes in

Answer 1

The probability that a randomly selected shot either hits the rim or goes in is 0.31.

Explanation:

The probability of the union of two events A and B is given by:

`P(A\cup B)=P(A)+P(B)-P(A\cap B)`

Denote the events as follows:

X = the ball hits the rim

Y = the ball goes in

The information provided is:

P (X) = 0.19

P (Y) = 0.17

P (X ∩ Y) = 0.05

Compute the value of P (X ∪ Y) as follows:

`P(X\cup Y)=P(X)+P(Y)-P(X\cap Y)`

`=0.19+0.17-0.05\\=0.31\\`

Thus, the probability that a randomly selected shot either hits the rim or goes in is 0.31.