What is the probability of exactly one tall student out of two students?

[neubreed]

Homework Statement

26 out of 50 total students are tall. If 2 different students are called on at random, what is the probability that exactly one is tall?

Homework Equations

please see below

The Attempt at a Solution

so here's what I ended up with:
1st student is tall: 26/50 x 24/49=312/1225
2nd student is tall: 24/50 x 26/49= 312/1225

I'm not sure whether I now multiply the two fractions or add them... Am I on the right track?

Thanks!

 

[Dick]

Homework Statement

26 out of 50 total students are tall. If 2 different students are called on at random, what is the probability that exactly one is tall?

Homework Equations

please see below

The Attempt at a Solution

so here's what I ended up with:
1st student is tall: 26/50 x 24/49=312/1225
2nd student is tall: 24/50 x 26/49= 312/1225

I'm not sure whether I now multiply the two fractions or add them... Am I on the right track?

Thanks!

Yes, if you want to do it that way you are on exactly the right track. The two events you have are mutually exclusive. What do you think about the question of whether to add or multiply?

 

[neubreed]

I'm leaning towards adding, but the end result seems a little high... Would 624/1225 be the asnwer?

 

[HallsofIvy]

Why is that "high"? It is just about 1/2 and just about 1/2 of the students are "tall".

If A and B are "equally likely" (probability of each 1/2) then "AA", "AB", "BA", and "BB" all have probability 1/4 so AB+ BA has probability 1/2.

 

[Dick]

I'm leaning towards adding, but the end result seems a little high... Would 624/1225 be the asnwer?

Yes, it is. You can check it using the combinations formula C(n,k) if you know that. There are C(26,1) ways to choose the tall, C(24,1) ways to choose the other and C(50,2) ways total ways to choose 2 students. C(26,1)*C(24,1)/C(50,2)=624/1225.