A basketball team at a university is composed of ten players. The team is made u

Question

A basketball team at a university is composed of ten players. The team is made up of players who play either guard, forward, or center position. Four of the ten are guards; four of the 10 are forwards; and two of the ten are centers. The number of the players are 1, 2, 3, 4, for the guards; 5, 6, 7, 8 for the forwards; and 9 and 10 for the centers. The starting five are numbered 1, 3, 5, 7, and 9. Let a player be selected at random from the ten. Define the following events:

A= player selected has a number 1 to 8

B= player selected is a guard

C= player selected is a forward

D= player selected is a starter

E= player selected is a center

P (A or E) equal to

1.0      B. 0.80           C. 0.60           D. 0.50          E. 0.20

please show step by step how to solve

Explanation / Answer

Number of ways selecting a player out of 8 numbered 1 to 8 is 1. So the probability of event A is

P(A) = 8/10 = 0.8

There are two center player 9 and 10 so the probability of event B is

P(E) = 2/10 = 0.2

Since A and E cannot happened simultaneously so

P(A and E) = 0

Therefore

P(A or E) = P(A) + P(E) - P(A and E) = 1.0

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