Question

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

Answer 1

The total number obtained in the first throw of the dice = 6

And the case of not getting an odd number = 3

∴ Probability of not getting an odd number in the first toss P(A) = `3/6 = 1/2`

Similarly, the probability of not getting an odd number in the second toss is P(B) = `1/2`

Probability of not getting an odd number in the third toss P(C) = `1/2`

∵ The above three events are independent.

∴ The probability of all three happening together i.e. the event of not getting an odd number in each toss

P(A ∩ B ∩ C) = P(A) . P(B) . P(C)

= `1/2 . 1/2 . 1/2`

= `1/8`

∴ Probability of getting an odd number at least once

= 1 − P(A ∩ B ∩ C) 

= `1 - 1/8`

= `7/8`