A study of the incoming freshman class at a university found that 60% of the stu

Question

A study of the incoming freshman class at a university found that 60% of the students had taken AP Calculus in high school, 55% had taken AP English in high school, and 20% had taken both AP Calculus and AP English. One incoming freshman is randomly selected from the population of incoming freshman. Let C = the selected student took AP Calculus E = the selected student took AP English.What is the probability that the selected incoming freshman did not take AP Calculus nor AP English? provide steps please

Explanation / Answer

Here, we are given that: P(C) = 0.6, P(E) = 0.55 and P(C and E) = 0.2

Using law of total addition, we get:

P(E or C) = P(C) + P(E) - P(E and C) = 0.6 + 0.55 - 0.2 = 0.95

Therefore P( neither E nor C) = 1 - P(E or C) = 1- 0.95 = 0.05

Therefore 0.05 is the probability that the selected incoming freshman did not take AP calculus nor AP english.

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