To find the probability that you stop at the second traffic light given that you stop at the first traffic light, you need to use conditional probability. The formula for conditional probability is:
P(A|B) = P(A∩B) / P(A)
In this case, we want to find P(B|A), which is the probability of stopping at the second traffic light given that you stop at the first traffic light. Plugging in the given values:
P(B|A) = P(A∩B) / P(A)
P(B|A) = 0.3 / 0.4
P(B|A) = 0.75
Therefore, the probability that you stop at the second traffic light given that you stop at the first traffic light is 0.75 or 75%.
On my commute to work, I pass through two intersections with traffic lights. Based on a large amount of empirical data, I estimate that:
- the probability I stop at the first traffic light (event A) is 0.4
- the probability I stop at the second traffic light (event B) is 0.5,
- and the probability that I stop at both traffic lights (A∩B) is 0.3.
Given that I stop at the first traffic light, what is the probability that I also stop at the second?
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