Probability of being selected to win a prize.

Question

At an event there are 4 children and 6 adults, three of them will be randomly selected to win a prize. What will be the probability that there is one adult and two children that win the prize?

Answer 1

(4 choose 2)(6 choose 1) / (10 choose 3) =

numerator is (4*3)/2 * 6 = 36

denominator is (10*9*8)/(3*2*1) = 720/6 = 120

36/120 = 3/10 = 0.3

Answer 2

Hi Ashley

The way this problem is worded, the order of selection of the prizewinners doesn't matter, so this is a problem using Combinations. The probability is calculated as a numerator over a denominator. The denominator is the number of ways that that 3 people can be selected from a group of 10 ( 6 adults and 4 kids). That number is the combination of 10 things taken 3 at a time. I'm sure you can calculate that.

The numerator is the product of two events - two children selected from four and one adult selected from 6. They are multiplied together because they are independent of each other.

So the equation is [C(4,2)*C(6,1)] / C(10,3) It's a pretty small probability - I got 3/70

Hope that helps!