Question

A fair die is tossed repeatedly until a six is obtained. Let x denote the number of tosses required. The probability that x 3 equals

Answer 1

The probability that the fair die obtains a six at x=3 is 25/216.

• A fair die is tossed repeatedly until a six is obtained.
• x denotes the number of tosses required to obtain six on the die
• We have to find the probability that the fair die obtains a six on the third time.

Probability that the fair die does not obtain six is 5/6.

Probability that the fair die obtains a six is 1/6.

• Therefore,

Probability that the dice obtains six on third time is

P(x=3) = (5/6)(5/6)(1/6)       [The last one is (1/6) as the obtained number is a six]

P(x=3) = 25/216