# Packaging Error

• Nov 12th 2010, 03:22 PM
cristinaivelisse
Packaging Error
I need help with this exercise. I don't understand what probability rule I have to used with it.

Because of a mistake in packaging, a case of 12 bottles of red wine contained 5 Merlot and 7 Cabernet, each without labels. All the bottles look alike and have an equal probability of being chosen. Three bottles are random selected.

a) What is the probability that all 3 are Merlot?
b) What is the probability that exactly two are Merlot?
c) what is the probability that none is a Merlot?
• Nov 12th 2010, 03:54 PM
harish21
There are 5 Merlot and 7 Cabernet bottles. Since all bottles look alike,

(a) the probability for the first bottle being Merlot is 5/12. If one bottle drawn out of 12(which is a Merlot), there are 11 bottles left and your probability for the second bottle being Merlot is (4/11). Likewise, the third one being Merlot is (3/10)

so, $\displaystyle \mbox{P(all 3 are Merlot)} = \dfrac{5}{12}\times\dfrac{4}{11} \times \dfrac{3}{10}=..$

use the same concept for (b) and (c) and show your work if you have any queries!