The following problem is given accordingly:
The path used by a certain Canada Post mailman to deliver mail to the University of Guelph includes two intersections with traffic signals. Probability of the event that he will have to stop at the first intersection is 0.35; and the probability that he will need to stop at the second one is 0.65. Furthermore, probability of making a stop at at least one of the two intersections is 0.7. What is the possibility that:
a) He will stop at both intersections?
b) The second intersection given that he stopped at the first one? Is this different from 0.65?
In this problem stated that P(AUB) = 0.7. However, if the problem was independent, P(AUB) = 0.7725.
I argued the fact that in order for the probabilities to be independent, the driver's chances at stopping on the second intersection would have to be the same before and after he was stopped at the first intersection. Realistically speaking however, this would not be the case hence I assumed that they were dependent.
If the lights are independent, why so and is there a way to prove this mathematically?