Question

There are 7 students running for 2 seats on student council. If each student is equally likely to be elected, what is the probability that Megan will be elected president and Javier will be elected vice president?

Answer 1

I respectfully disagree with the answer above.

There are two ways to approach this question; you can do it logically or apply permutations:

Logically, when Megan receives a position, then the possible number of students will decrease from 7 to 6. This means that 6 students are now competing for vice president, and now the denominator changes. Hence...

Let P(M)=Probability Megan receives president
Let P(J) = probability Javier receives vice president

\(P(M)=\frac{1}{7}\)
\(P(J)=\frac{1}{6}\)
\(∴P(M⋂J)=P(M)P(J)=\frac{1}{7}\times\frac{1}{6}=\frac{1}{42}\)

The more conventional method is to realize that the scenario much resembles a permutation. Order matters here in the number of possible selections, so it is not a combination, but a permutation. You can then just employ the permutation formula:

\(_nP_r\) where n=no. of objects and r=selections dependent on order
here n=7 and r=2
∴\(_{7}P_2\) is representative of this scenario.
You will get that as 42, so that's the total number of permutations. This means that the actual probability is 1/42

Answer 2

Oh, yes, you are right. I was looking at the probability in terms of a whole. I forgot to distinguish them. The person above is correct, after checking my work, I see that.

Answer 3

It's okay man it happens :D

Answer 4

Yeah, it was 1 AM when I did that answer HAHA

Answer 5

I can relate to your experience lol

Answer 6

Yeah, i am actually surprised I couldn't do it better, I am best at Computer Science, I do probability all the time XD

Answer 7

Well, majorly hacking, but...

Answer 8

Noice

Answer 9

Interesting