Question

A die is tossed thrice. Find the probability of getting an odd number at least once.

Answer 1

Let, the probability to get an even number is A.

The probability to get an odd number at least once P=1−P( AAA ).

The probability is given as,

P( AAA )=P( A )×P( A|A )×P( AA|A )(1)

Here, the probability to get an even number is P( A ), the probability to get even number on second chance after first chance is succeed is P( A|A ) and the probability to get even number on third chance after first two chances are succeed is P( AA|A ).

The even numbers on a die will be { 2,4,6 }=3 and total numbers will be 6.

P( A )= 3 6 = 1 2 P( A|A )= 3 6 = 1 2 P( AA|A )= 3 6 = 1 2

Substitute the given values in the equation (1) we get.

P( AAA )= 1 2 × 1 2 × 1 2 = 1 8

The probability to get an odd number at least once is,

P=1−P( AAA ) =1− 1 8 = 7 8

Thus, the probability to get an odd number at least once is 7 8 .