Answer to Question #349992 in Statistics and Probability for sunny

Question

Let the probability that a successful rocket launching will be equal to 0.4. Find,

Average number of trials required for the successful rocket launching.

The probability that the successful launching will be made on the third attempt.

The probability that successful rocket launching requires less than 5 attempts.

Answer 1

Let $X=$ the number of attempts: $X\sim G(p).$

Given $p=0.4.$

1.

$$\mu=E(X)=\dfrac{1-p}{p}=\dfrac{1-0.4}{0.4}=1.5$$

2.

$$P(X=3)=(1-0.4)^2(0.4)=0.144$$

3.

$$P(X<5)=P(X\le 4)$$

$$=1-(1-0.4)^4=0.8704$$