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 the first traffic light but not the second?
To find the probability that you stop at the first traffic light (event A) but not the second (not event B), we need to subtract the probability of stopping at both traffic lights (A∩B) from the probability of stopping at the first traffic light (event A).
P(A∩B) = 0.3 (probability of stopping at both traffic lights)
P(A) = 0.4 (probability of stopping at the first traffic light)
To find the probability of stopping at the first traffic light but not the second, we subtract P(A∩B) from P(A):
P(A and not B) = P(A) - P(A∩B)
= 0.4 - 0.3
= 0.1
Therefore, the probability that you stop at the first traffic light but not the second is 0.1.
To find the probability that you stop at the first traffic light (A) but not the second (B), you need to subtract the probability of stopping at both traffic lights (A∩B) from the probability of stopping at the first traffic light (A) only.
In this case, the probability you stop at the first traffic light (A) is 0.4, and the probability you stop at both traffic lights (A∩B) is 0.3.
Therefore, the probability you stop at the first traffic light but not the second is:
P(A but not B) = P(A) - P(A∩B)
= 0.4 - 0.3
= 0.1
So, the probability that you stop at the first traffic light but not the second is 0.1 or 10%.
To find the probability that you stop at the first traffic light (event A) but not the second (event B), you can use the concept of conditional probability. Conditional probability is the probability of an event occurring given that another event has already occurred.
We know that the probability of stopping at both traffic lights (A∩B) is 0.3. We also know that the probability of stopping at the first traffic light (event A) is 0.4. Therefore, to find the probability of stopping at the first traffic light but not the second, you can subtract the probability of stopping at both traffic lights (A∩B) from the probability of stopping at the first traffic light (event A).
Here's how to calculate it:
P(A but not B) = P(A) - P(A∩B)
P(A but not B) = 0.4 - 0.3
P(A but not B) = 0.1
So, the probability that you stop at the first traffic light but not the second is 0.1, or 10%.