Question

A bag contains 10 marbles numbered from 1 to 10. Two marbles are selected from the bag at the same time. Let event E = the two numbers are even. How many outcomes are in the complement of E?
A.10
B.20
C.60
D.80

Answer 1

D) 80

because

total outcomes = 10 x 9 = 90

the numbers are even,

(2, 4), (2, 6), (2, 8), (2, 10), (4, 6), (4, 8), (4, 10), (6, 8), (6, 10), (8, 10)

The complement of E is when the two numbers are NOT even.

thus,

90 - 10 = 80

Answer 2

Answer: 80

Step-by-step explanation:

Given: Number of marbles in the bag = 10

When two marbles are selected from the bag at the same time i.e. repetition is not allowed.

Now, the number of possible ways to select two marbles at same time is given by :-

$^{10}P_2=\frac{10!}{(10-2)!}=\frac{10\times9\times8!}{8!}=90$

Let E be the event of drawing the two numbers that are even.

Then, the number of possible ways to select two marbles is given by :

$^5C_2=\frac{5!}{2!(3!)}=\frac{120}{2\times6}=10$

Now, the number of outcomes in the complement of E$=90-10=80$