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?

Answer 1

Answer:

1/2.

Step-by-step explanation:

Let O = an odd number and E an even number.

The possible outcomes for  an odd sum are:

OOO

OEE

EOE

EEO

The probability of an odd on each pick = 50/100 = 1/2 and for an even it is also 1/2.

Prob( O O O) = 1/2*1/2*1/2 = 1/8.

The probability for the other 3 possible outcomes is also 1/8 , therefore the probability  for odd number totals = 4 * 1/8

= 1/2.