Question
A die is thrown again and again until three sixes are obtained. Find the probability of obtaining the third six in the sixth throw of the dice.
Solution
A die is thrown again and again.
Probability of getting a six in a throw =
Probability of not getting a six in a throw =
Since third six is in sixth throw
∴ there are two sixes in first five throws and one six in the sixth throw.
Probability of getting two sixes in 5 throws =
Probability of getting a six in sixth throw =
∴ probability of getting a third six in the sixth throw
Probability of getting a six in a throw =
Probability of not getting a six in a throw =
Since third six is in sixth throw
∴ there are two sixes in first five throws and one six in the sixth throw.
Probability of getting two sixes in 5 throws =
Probability of getting a six in sixth throw =
∴ probability of getting a third six in the sixth throw
