2007 H2 Mathematics
Paper 2 Question 10
A player throws three darts at a target. The probability that he is successful in hitting the target with his first throw is For each of his second and third throws, the probability of success is
- twice the probability of success on the preceding throw if that throw was successful,
- the same as the probability of success on the preceding throw if that throw was unsuccessful.
(a)
Construct a probability tree showing this information.
[3]
(b)
Find
(i)
the probability that all three throws are successful,
[2]
(ii)
the probability that at least two throws are successful,
[2]
(iii)
the probability that the third throw is successful given that exactly two of the three throws are successful.
[4]