Question

A bag contains 11 blocks numbered from 1 to 11. Two blocks are selected from the bag at the same time. (order does not matter) Let event E = the two numbers are odd. How many outcomes are in the complement of E? A) 40 B) 30 C) 25 D) 20

Answer 1

(A) n(Eᶜ)=40

Explanation:

The Sample Space for is given as:

(1,2),(1,3),(1,4),(1,5),(1,6),(1,7),(1,8),(1,9),(1,10),(1,11)

(2,3),(2,4),(2,5),(2,6),(2,7),(2,8),(2,9),(2,10),(2,11)

(3,4),(3,5),(3,6),(3,7),(3,8),(3,9),(3,10),(3,11)

(4,5),(4,6),(4,7),(4,8),(4,9),(4,10),(4,11)

(5,6),(5,7),(5,8),(5,9),(5,10),(5,11)

(6,7),(6,8),(6,9),(6,10),(6,11)

(7,8),(7,9),(7,10),(7,11)

(8,9),(8,10),(8,11)

(9,10),(9,11)

(10,11)

n(S)=55

Event E is the Event that the two numbers are odd.

Therefore: Complement of E will be the event that any of the two numbers is even.

The Sample Space of the complement of E is:

`(1,2),(1,4),(1,6),(1,8),(1,10)\\(2,3),(2,4),(2,5),(2,6),(2,7),(2,8),(2,9),(2,10),(2,11)\\(3,4),(3,6),(3,8),(3,10)\\(4,5),(4,6),(4,7),(4,8),(4,9),(4,10),(4,11)\\(5,6),(5,8),(5,10)\\(6,7),(6,8),(6,9),(6,10),(6,11)\\(7,8),(7,10)\\(8,9),(8,10),(8,11)\\(9,10)\\(10,11)\\`

Therefore:

n(Eᶜ)=40