1 Two students Cassie and Jerry were enrolled in the same cl

1.) Two students, Cassie and Jerry, were enrolled in the same class. The professor conducted a study at the end of the semester and found that the probability that Cassie was absent from class on any day is 0.3, the probability that Jerry was absent from class any day is 0.4, and the probability that both Cassie and Jerry were absent from class on the same is 0.2.

A.) What is the probability that on any given day, either Cassie or Jerry was absent from class?

B.) What is the probability that Cassie was absent from class and Jerry was present on any day?

C.) Given that only one of them was in class on a particular day, what is the probability that it was Jerry.?

Solution

Let

C= Cassie is absent
J = Jerry is absent

a)

P(C or J) = P(C) + P(J) - P(C and J)

Thus,

P(C or J) = 0.3+0.4-0.2 = 0.5 [answer]

**********

b)

P(C and J\') = P(C) - P(C and J) = 0.3 - 0.2 = 0.1 [answer]

***********

c)

P(J| only one) = P(C and J\') / [P(C and J\') + P(C\' and J)

As

P(C\' and J) = P(J) - P(C and J) = 0.4 - 0.2 = 0.2,

P(J| only one) = P(C and J\') / [P(C and J\') + P(C\' and J) = (0.1) / (0.1+0.2) = 0.33333333 [answer]