7 Jenny has six darts. She throws darts, one at a time, aiming each at the bull's-eye. The probability that she hits the bull's-eye with her first dart is 0.1 . For any subsequent throw, the probability of hitting the bull's-eye is 0.2 if the previous dart hit the bull's-eye and 0.05 otherwise.
- Illustrate the possible outcomes for her first, second and third darts on a probability tree diagram.
- Find the probability that
(A) she hits the bull's-eye with at least one of her first three darts,
(B) she hits the bull's-eye with exactly one of her first three darts. - Given that she hits the bull's-eye with at least one of her first three darts, find the probability that she hits the bull's-eye with exactly one of them.
Jenny decides that, if she hits the bull's-eye with any of her first three darts, she will stop after throwing three darts. Otherwise she will throw all six darts.
- Find the probability that she hits the bull's-eye three times in total.