Question

a bag contains 6 cherry, 3 orange, and 2 lemon candies. You reach in and take 3 pieces of candy at random. The probability that you have 1 cherry candy and 2 lemon candies is what?

Answer 1

How far have you gotten?

Answer 2

I havent gotten anything yet

Answer 3

Try starting by finding the probabilities of drawing each kind of candy.

Answer 4

There are 3 different types of candies.

Answer 5

Is this for a class? Or is this just a random question? I'm just curious because I don't want to just do the work for you, rather help you with finding the solution.

To start. There are how many candies total? That is your denominator for your probabilities.

Answer 6

Here is the denominator. There are 11 chose 3 ways to draw 3 candies from the jar. \[\left(\begin{matrix}11 \\ 3\end{matrix}\right)\]

Answer 7

Got the numerator?

Answer 8

Hint: use reasoning similar to the denominator, but realize your are choosing from a collection of smaller samples. Not the full 11.

Answer 9

Just a random question in a game we are playing

Answer 10

Ah. Did anyone get a solution? The answer is \[\frac{ \left(\begin{matrix}6 \\ 1\end{matrix}\right)\left(\begin{matrix}2 \\ 2\end{matrix}\right) }{ \left(\begin{matrix}11 \\ 3\end{matrix}\right) }\]

Answer 11

someone got 0.1212 so which one is correct? Its a debate now to find the correct answer

Answer 12

Well, most clearly there are 11 choose 3 possible ways to pick the candies total. So 165. Thats the denominator.

Now. Imagine that the candies were unique. So the cherry candies have the numbers 1-6 on them, and the lemons have a 1 and a 2. If you list the possible combinations of The candies that meet the criteria given you have:

Cherry Lemon
1 1,2
2 1,2
3 1,2
4 1,2
5 1,2
6 1,2

Answer 13

So there are 6 total possible combinations that satisfy being 1 cherry 2 lemon. 6/165 = .0363636 or (6 choose 1)(2 choose 2) / (11 chose 3)

Answer 14

Oh....okay now that makes since! Thanks :-)

Answer 15

Any time, glad to help!