# Thread: quick question on probability of AT LEAST and EXACTLY

1. ## 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?

2. 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 $\displaystyle \Pr(A \cup B)$. There is a formula for this, which you have clearly used. Your calculation is correct.

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

4. 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).