Question

A bag contains 12 balls numbered from 1 to 12. Two balls are selected from the bag one at a time, without replacement. (order matters) Let event E = the two numbers have a sum of 5. How many outcomes are in the complement of E?

Answer 1

I believe you have to divide

Answer 2

There are 128 outcomes in the complement of E

Explanation:

Given that a bag contains 12 balls numbered from 1 to 12. Two balls are selected from the bag one at a time, without replacement. (order matters)

Possibilities of getting sum of 5 is drawing in this order

(1,4) (2,3) (3,2) (4,1) = 4 ways

Total no of ways of drawing 2 balls from 12 balls where order matters

= 12P2

= 132

Thus we have

n(E) = 4

n(sample space ) =132

Hence

n(E') =
`132-4=128`

There are 128 outcomes in the complement of E