Answer to Question #255753 in Statistics and Probability for orko

Question

If a fair coin is successively flipped, find the probability that a head first appears on the fifth trial.

Answer 1

In this case we have a geometric distribution

$$g(x, p)=pq^{x-1}$$

Gicen $p=\dfrac{1}{2}=q, x=5$

$$P(X=5)=\dfrac{1}{2}(\dfrac{1}{2})^{5-1}=\dfrac{1}{32}$$

The probability that a head first appears on the fifth trial is $\dfrac{1}{32}.$