Answer to Question #344874 in Statistics and Probability for Akshay

Question

Youre trying your hand at snowboarding and observe the probability that the other snowboarder will make it down the slope without falling over is 0.4. What is the probability that you will need more than 4 attempts to be successful?

Answer 1

Geometric Distribution

If repeated independent trials can result in a success with probability $p$ and

a failure with probability $q = 1 - p,$ then the probability distribution of the

random variable $X,$ the number of the trial on which the first success occurs, is

$$g(x; p) = pq^{x-1}, x = 1, 2, 3, . . . .$$

Given $p=0.4, q=1-p=0.6$

$$P(X=1)=0.4(1)=0.4$$

$$P(X=2)=0.4(0.6)=0.24$$

$$P(X=3)=0.4(0.6)^2=0.144$$

$$P(X=4)=0.4(0.6)^3=0.0864$$

$$P(X>4)=1-0.4-0.24-0.144-0.0864$$

$$=0.1296$$