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:
[tex]P(J\ and\ N) = 0.265[/tex]
Step-by-step explanation:
Given
Represent Junior with J and Nursing Major with N.
So, we have:
[tex]P(N) = 0.15[/tex]
[tex]P(J) = 0.20[/tex]
[tex]P(J\ or\ N) = 0.085[/tex]
Required
Determine [tex]P(J\ and\ N)[/tex]
In probability, for events A and B
[tex]P(A\ and\ B) = P(A) + P(B) - P(A\ or\ B)[/tex]
In this case:
[tex]P(J\ and\ N) = P(J) + P(N) - P(J\ or\ N)[/tex]
Substitute values for P(J), P(N) and P(J or N)
[tex]P(J\ and\ N) = 0.20 + 0.15 - 0.085[/tex]
[tex]P(J\ and\ N) = 0.265[/tex]
Hence, the probability that an undergraduate is a Junior and major in Nursing is 0.265
