Question

g The probability 0.15. The probability that is 0.085. What is the probability that a undergraduate is a Junior and a Nursing major

Answer 1

Question:

The probability that a UCR undergraduate majors in Nursing is 0.15. The  probability that a UCR undergraduate is a Junior is 0.20. The probability that a UCR  undergraduate is a Junior or a Nursing major is 0.085. What is the probability that a UCR  undergraduate is a Junior and a Nursing major?

Answer:

$P(J\ and\ N) = 0.265$

Step-by-step explanation:

Given

Represent Junior with J and Nursing Major with N.

So, we have:

$P(N) = 0.15$

$P(J) = 0.20$

$P(J\ or\ N) = 0.085$

Required

Determine $P(J\ and\ N)$

In probability, for events A and B

$P(A\ and\ B) = P(A) + P(B) - P(A\ or\ B)$

In this case:

$P(J\ and\ N) = P(J) + P(N) - P(J\ or\ N)$

Substitute values for P(J), P(N) and P(J or N)

$P(J\ and\ N) = 0.20 + 0.15 - 0.085$

$P(J\ and\ N) = 0.265$

Hence, the probability that an undergraduate is a Junior and major in Nursing is 0.265