Question

A bag has 10 yellow poker chips and 4 green poker chips. If you reach in to randomly draw 5 chips, what is the probability of selecting exactly 3 yellow chips and 2 green chips?

Answer 1

In the study of probability, you find the chances of an event to happen likely out of the total number of possibilities. Thus, probabilities are always presented as part of a whole: in terms of fractions or percentages. 

In this problem, the denominator for the probability would be the total number of possibilities. In combination probability, we use the equation: n!/r!(n-r)!, where 'r' is the number of like things out of 'n' objects. So, the denominator would be 5 drawn chips out of a total of 14 chips. So,

denominator = 14!/5!(14-5)! = 2,002 ways

For the numerator, we multiply the combination for 3 out of 10 chips and 2 out of 4 chips. 

Numerator = 10!/3!(10-3)! × 4!/2!(4-2)!
Numerator = 720 ways

Thus, the probability is

Probability = 720/2002 = 360/1001 or 35.96%