Answer to Question #233899 in Statistics and Probability for neil

Question

2.1 A grade 12 learner from Keetmanshoop is attempting to pass his driver’s test. The probability that he Passes on his first attempt is 3/5  . At any further attempt the probability that he passes is 9/10

(a) Draw a tree diagram that illustrates the probabilities of passing at the first, second or third attempt. [2]

(b) Find the probability that he needs no more than two attempts to pass the test.

Answer 1

(a)

(b) Let $X=$ the number of attempts.

$$P(X\leq2)=P(X=1)+P(X=2)$$

$$=\dfrac{3}{5}+(1-\dfrac{3}{5})(\dfrac{9}{10})=\dfrac{24}{25}=0.96$$