(a)
Dipak continues with the test until he passes. The random variable $X$ is the number of attempts Dipak needs in order to pass the test.
(a(i))[2]
Calculate $P(2 \leq X \leq 6)$.
(a(ii))[1]
Calculate $\text{E}(X)$.
(b)[3]
Five friends are each going to take their advanced driving test tomorrow. Find the probability that at least three of them pass tomorrow.
(c)[5]
Next week, seventy-five people will take their advanced driving test. Use an approximation to find the probability that more than $20$ of them pass next week.