To find the probability that you stop at neither of the traffic lights (A'∩B'), we can use the formula:
P(A'∩B') = 1 - P(A∪B)
First, let's find P(A∪B) using the formula for the union of two events:
P(A∪B) = P(A) + P(B) - P(A∩B)
P(A∪B) = 0.4 + 0.5 - 0.3
P(A∪B) = 0.6
Now, we can find P(A'∩B'):
P(A'∩B') = 1 - P(A∪B)
P(A'∩B') = 1 - 0.6
P(A'∩B') = 0.4
Therefore, the probability that you stop at neither of the traffic lights on your commute is 0.4 or 40%.
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.
What is the probability that I stop at neither of the traffic lights on my commute?
1 answer