Question

A box contains 100 balls, numbered from 1 to 100. If three balls are selected at random and with replacement from the box, what is the probability that the sum of the three numbers on the balls selected from the box will be odd?

A) 1/4
B) 3/8
C) 1/2
D) 5/8
E) 3/4

Answer 1

Option C.

Explanation:

It is given that a box contains 100 balls, numbered from 1 to 100.

Three balls are selected at random and with replacement from the box.

We need to find the probability that the sum of the three numbers on the balls selected from the box will be odd.

From 1 to 100, 50 numbers are odd and 50 numbers are even.

`P(Even)=(50)/(100)=(1)/(2)`

`P(odd)=(50)/(100)=(1)/(2)`

Probability = P(All three are odd) + P(Only first is odd) + P(only second is odd) + P(only third is odd)

`P=((1)/(2)* (1)/(2)* (1)/(2))+((1)/(2)* (1)/(2)* (1)/(2))+((1)/(2)* (1)/(2)* (1)/(2))+((1)/(2)* (1)/(2)* (1)/(2))`

`P=(1)/(8)+(1)/(8)+(1)/(8)+(1)/(8)`

`P=(4)/(8)`

`P=(1)/(2)`

Therefore, the correct option is C.