Let S be the event that a randomly selected college student has taken a statistics course, and let C be the event that the same student has taken a chemistry course. Suppose P (S) = 0.4, P(C) = 0.3, and P(S ∩ C) = 0.2.

a. Find the probability that a student has taken statistics, chemistry, or both.

b. Find the probability that a student has taken neither statistics nor chemistry.

c. Find the probability that a student has taken statistics but not chemistry.

Answer:

Step 1 of 4:

Let ‘S’ be the event that a randomly selected college student has taken a statistic course.

Let ‘C’ be the event that the same student has taken a chemistry course.

Given the probabilities are 4,

Step 2 of 4:

a). To find the probability that a student has taken statistics, chemistry or both.

That is,

[Since, by the addition rule

Then,

= 0.5.

Therefore, the probability that a student has taken statistics, chemistry or both subjects is 0.5.