PROBABILITY

Question

A bag contains 6 red balls and 6 blue balls. 5 balls are selected at random. Find the probability of selecting 5 red balls.

Answer 1

The question is a little bit ambiguous.  Let's assume you draw the balls out one at a time and do not put them back in before drawing the next one out.

 

The chance of choosing a red ball on your first draw is 6/12. The chance of choosing a red ball on your second draw is 5/11 (because now there are only 5 red balls left in there, and only 11 total). The chance of choosing a red ball on your third draw is 4/10. On your fourth draw it is 3/9. And on your 5th draw it is 2/8.

 

So 6/12 * 5/11 * 4/10 * 3/9 * 2/8. The answer is 720/95040.  This reduces to 1/132.

 

 

Answer 2

In this question, the wording suggests that the balls are not replaced after selection.

 

The probability of getting the first red ball is  6/12.

Once a red ball is picked the chance of getting a second red ball is 5/11

Assuming two red balls are picked the chance of getting the third red ball is 4/10.

 

The chances of getting five red balls is then  (6/12)(5/11)(4/10)(3/9)(2/8)  = 1/132

Answer 3

Alternatively, probability = 6C5/12C5 = 6/792 = 1/132