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

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Homework Help Overview

The problem involves calculating the probability of selecting exactly one tall student from a group of 50 students, where 26 are tall. Participants are discussing the appropriate method to determine this probability when two students are chosen at random.

Discussion Character

  • Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants explore the calculation of probabilities for two mutually exclusive events, considering whether to add or multiply the probabilities of different outcomes. There is discussion about the interpretation of the resulting probability and its implications.

Discussion Status

Some participants affirm that the approach taken is correct, while others express uncertainty about the final probability value. There is a suggestion to verify the result using combinations, indicating a productive direction in the discussion.

Contextual Notes

Participants are working under the constraints of a homework assignment, which may limit the information they can use or the methods they can apply. The discussion reflects varying levels of confidence in the calculations and interpretations of probability.

neubreed
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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!
 
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neubreed said:

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

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