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 die.
Answer:
Probability that getting a 6 in a throw of die p = 1/6
Probability that getting a 6 in a throw of die q = 1 - 1/6 = 5/6
Probability that 2 sixes come in the first five throws of the die = 5C2 * (1/6)2 * (5/6)3
= (10*125)/65
So probability that 3rd six come in the sixth throw = (10*125)/65 * 1/6
= (10*125)/46656
= 625/23328
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