Mrs. Goh drives to work. The route used by her contains three intersections with traffic signals. The probability that she must stop at the first signal is 0.4. The probability that she must stop at the second signal is 0.5. The probability that she must stop at third signal is 0.6. The probability that she must stop at at least one of the three signals is 0.9. The probability she must stop at at least one of the first two signals is 0.7. The probability she must stop at at least one of the last two signals is 0.8. Finally, the probability she must stop at at least one of the first and third Signals is also 0.8.
a) What is the probability that she must stop at all signals?
b) At exactly one signal?