A fair coin is tossed repeatedly until two consecutive heads are obtained. If the probability that 2 consecutive heads occur on fourth and fifth toss is p , then 30 p is equal to

Step-by-step solution

Fourth and fifth toss turns up head hence tail must occur on third toss. So, H T , T H or T T occurs on the first and second toss. Hence, the required probability = 1 2 × 1 2 × 1 2 × 1 2 × 1 2 ⏟ H T T H H + 1 2 × 1 2 × 1 2 × 1 2 × 1 2 ⏟ T H T H H + 1 2 × 1 2 × 1 2 × 1 2 × 1 2 ⏟ T T T H H = 3 32