Thread: quick question on probability of AT LEAST and EXACTLY

The probability that student A will fail is .5, the probability that student B will fail is .2, and the probability that both will fail is .1. So..

P(A)=.5 P(B)=.2 P(AB)=.1

What is the probability that at least one student will fail?
Exactly one student will fail?

I did .5+.2-.1= .6 for P of at least one. I'm not sure if this is right or if it is for exactly one student instead. Any help please?

Originally Posted by holly123

The probability that student A will fail is .5, the probability that student B will fail is .2, and the probability that both will fail is .1. So..

P(A)=.5 P(B)=.2 P(AB)=.1

What is the probability that at least one student will fail?
Exactly one student will fail?

I did .5+.2-.1= .6 for P of at least one. I'm not sure if this is right or if it is for exactly one student instead. Any help please?

You require . There is a formula for this, which you have clearly used. Your calculation is correct.

Thanks, I was just wondering if I should do that for "at least one" or "exactly one" or both?

Originally Posted by holly123

Thanks, I was just wondering if I should do that for "at least one" or "exactly one" or both?

Exactly one means calculating Pr(A and B') + Pr(A' and B).