Answer:
a. 0.6975
b. 0.25
c. The events are independent and inclusive
Step-by-step explanation:
a. The proportion of five-star football recruits in the nation that go to universities in the three most competitive athletic conferences = 75%
Therefore, the probability of a five-star football recruits chooses to go to a university in the three most competitive athletic conferences p(A) = 75% or 0.75
The proportion of the times five-star football recruits get full football scholarships = 93%
Therefore, the probability that a five-star football recruit get full football scholarships p(B) = 93% or 0.93
Therefore, the probability that a randomly selected five-star recruit who chooses one of the best three conferences will be offered a full football scholarship can be written as -the probability that a randomly selected five-star recruit who chooses one of the best three conferences and will be offered a full football scholarship is therefore;
p(A) ∩ p(B) = p(A) × p(B) = 0.75×0.93 = 0.6975
b. The probability that a randomly selected five star recruit will not select a university from one of the three best conferences = 1 - p(A) = 1 - 0.75 = 0.25
c. The events are independent as the given probability of occurrence of one event does not alter the probability of the other event
The events are inclusive events are exclusive events as P(A)and P(B) can take place simultaneously.
