Question : Jane wants to do her MSc in statistics. She appliesa to two universities. Assume the acceptance rate at University A is 25% and at University B is 35%. Further assume that acceptance at two universities are independent events.

a. What is the probability that Jane will be accepted by both universities?
b. What is the probability that neither university will accept Jane?
c. What is the probability that Jane will be accepted by at least one of the two universities?
d. What is the probability that one and only one will accept Jane?

Thanks in advance for the solution, Edwim

Edwim,

Welcome to Talk Stats. I will do part a and give the formula for b,c d.

a.
Since A and B are independent,
P(A and B)=P(A)*P(B)
=0.25*0.35
=0.0875

b.
P(neither A nor B)=1-P(A or B)
=1-[P(A)+P(B)-P(A and B)]

c.
P(at least one)=P(A or B)
=P(A)+P(B)-P(A and B)

d.
P(one and only one)=P(A but not B)+P(B but not A)
=[P(A)-P(A and B)] + [P(B)-P(A and B)]

Thanks Quark for you help. I only need the formulas. It seems so confusing at times. I thought P( at least one)= P(A and not B) + P(B and not A) + P(A and B).
Does at least one mean one or the other or both? Thanks.

Yes. at least one means one or the other or both.

b.
P(neither A nor B)=1-P(A or B)
=1-[P(A)+P(B)-P(A and B)]

how would it look like mathematically? i mean P(A and B),P(A or B),i.e calculation?