Question 1199635: A survey of athletes at a high school is conducted, and the following facts are discovered: 34% of the athletes are football players, 58% are basketball players, and 14% of the athletes play both football and basketball. An athlete is chosen at random from the high school: what is the probability that the athlete is either a football player or a basketball player?
Probability =
% (Please enter your answer as a percent)
Answer by ikleyn(52781)   (Show Source):
You can put this solution on YOUR website! .
(1) Question "either F or B" literally means "(F or B separately, EXCLUDING F and B simultaneously)".
Under this understanding, P(either F or B) = (P(F) - P(both)) + (P(B) - P(both)) =
= (0.34 - 0.14) + (0.58 - 0.14) = 0.64 = 64%. ANSWER
(2) Question "F or B" is close, but DIFFERENT. It literally means "(F or B, including F and B simultaneously)".
Under this understanding, P(F or B) = P(F) + P(B) - P(both) =
= 0.34 + 0.58 - 0.14 = 0.78 = 78%. ANSWER
So, even small differences may lead to different results.
Therefore, the reader should be very attentive and very confident
in the meaning of the question to answer it in a right way.
Solved.
|
|
|
