basic prob. questions

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September 27th 2009, 12:19 PM
jimmyp

basic prob. questions

A box contains 24 yellow, 25 green and 27 red jelly beans.
If 15 jelly beans are selected at random, what is the probability that:
a) 5 are yellow?
b) 5 are yellow and 9 are green?
c) At least one is yellow?

I'm unsure of the techniques needed for these, any suggestions are welcome. :)
September 27th 2009, 03:47 PM
APOC197777

Jelly beans probability question

A box contains 25 yellow, 27 green and 29 red jelly beans.
If 10 jelly beans are selected at random, what is the probability that:

6 are yellow?

6 are yellow and 3 are green?

At least one is yellow?
September 27th 2009, 05:06 PM
Plato

Quote:

Originally Posted by APOC197777

A box contains 25 yellow, 27 green and 29 red jelly beans.
If 10 jelly beans are selected at random, what is the probability that:
6 are yellow?
6 are yellow and 3 are green?
At least one is yellow?

There are $\binom{81}{10}$ ways to select these ten jelly beans.
There are $\binom{25}{6}\binom{56}{4}$ ways to select exactly 6 are yellow jelly beans..

Can you finish?
September 28th 2009, 05:19 AM
The Second Solution

Quote:

Originally Posted by jimmyp

A box contains 24 yellow, 25 green and 27 red jelly beans.
If 15 jelly beans are selected at random, what is the probability that:
a) 5 are yellow?
b) 5 are yellow and 9 are green?
c) At least one is yellow?

I'm unsure of the techniques needed for these, any suggestions are welcome. :)

a) $\frac{{24 \choose 5} \cdot {52 \choose 10}}{{76 \choose 15}}$

b) $\frac{{24 \choose 5} \cdot {25 \choose 9} \cdot {27 \choose 1}}{{76 \choose 15}}$

c) 1 - Pr(none are yellow).