Friday

March 27, 2015

March 27, 2015

Posted by **Hannah** on Wednesday, April 13, 2011 at 5:37pm.

If 13 jelly beans are selected at random, what is the probability that:

a) 5 are yellow?

b) 5 are yellow and 7 are green?

c) At least one is yellow?

- probability and counting -
**MathMate**, Thursday, April 14, 2011 at 12:04pmIn total, there are 25+28+38=91 jelly beans.

Using (n,r) to stand for "n choose r"

=n!/(r!(n-r)!)

To choose y yellow, g green and r red jelly beans, the number of ways to choose is given by

(25,y)*(28,g)*(38,r)

and the number of ways to choose the same number of jelly beans irrespective of colour is

(25+28+38,y+g+r)=(91,y+g+r)

So the probability is:

(25,y)*(28,g)*(38,r) / (91,y+g+r)

For 5 yellow, we not worry about the other two colours, so they can be combined, call it x. We need 8 of x.

Probability

=(25,5)*(66,8)/(91,13)

=53130*5743572120/1917283000904460

=0.1592 (approx.)

For (b), it is a similar expression. I get approx. 0.0012

For (c), you would choose 13 out of green and red, and subtract from the probability of 1.

1-(66,13)(25,0)/(91,13)

=1-0.01

=0.99 (approximately)

See also following link for a detailed explanation:

http://mathforum.org/library/drmath/view/69151.html

**Answer this Question**

**Related Questions**

math - The ratio of red jelly beans to yellow jelly beans in a dish is 2:3. If I...

math - danielle has 30 jelly beans and 18 green jelly beans. What is the ratio ...

Math - The ratio of red jelly beans to yellow jelly beans in a dish is 3:4. If ...

statistics - Four jelly beans are selected, one at a time from a bowl containing...

Probability - A jar contains four red, four yellow, and three green jelly beans...

Math - The ratio of red jelly beans to yellow jelly beans in a dish is 3:4. if ...

Math - A box has 8 blue and 5 green jelly beans. A bag has 6 blue and 8 green ...

math - The ratio of red jelly beans to yellow jelly beans in a dish is 3.4. If ...

math - Results of a survey of fifty students indicate that 30 like red jelly ...

math - one bag of jelly beans contains 14 red jelly beans. how many red jelly ...