Question

Mark and 74 other adults entered a raffle at the local community center where several prizes will be given. Twenty teenagers entered the raffle as well. What is the probability that the first 2 names drawn at the raffle will be those teenagers?

Answer 1

Please help

Answer 2

Come on mate

Answer 3

There's a couple of ways to figure this out. The easiest conceptually (though just slightly longer) is to see first how many ways 2 teenagers can be selected from among 20 teenagers. That is 20C2 (20 Combination 2). That would be the numerator.

The denominator is how many ways any 2 people can be selected from the total # of people (# of people is 95). So, the denominator is 95C2.

Answer: (20C2) / (95C2) which is:\[\frac{ \frac{ 20 \times 19 }{ 2 } }{ \frac{ 95 \times 94 }{ 2 } } = \frac{ 2 }{ 47 }\]

Answer 4

So, conceptually, you are looking at "2 teenagers" / "any 2 people" as the fraction.

Answer 5

Yes mate, but my teacher said to set it up as a proportion, so how do I do that

Answer 6

I'm not sure how she did it that way, but I can show you the other way I know how.

Answer 7

Ok sure

Answer 8

We are looking at a "pick of 2" so order does not matter, so we are dealing with combinations, not permutations. But for this method, let's start out with order.

The probability that your first pick is a teenager is

20/95.

This leaves 94 people among which are 19 teenagers, so the probability that the second one is a teenager is:

19/94

Multiply those 2 together:

(20/95)(19/94) = 2/47

Answer 9

Thank you very much mate!!!

Answer 10

You're welcome, and sorry for the slow typping.

Answer 11

It's ok