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 one or more traffic lights on my commute?
To find the probability that you stop at one or more traffic lights on your commute, we can use the principle of inclusion-exclusion.
First, let's find the probability that you stop at the first traffic light or the second traffic light. This can be calculated using the formula:
P(A∪B) = P(A) + P(B) - P(A∩B)
P(A∪B) = 0.4 + 0.5 - 0.3
P(A∪B) = 0.6
So, the probability that you stop at the first traffic light or the second traffic light is 0.6.
Since we are interested in the probability of stopping at one or more traffic lights (A∪B) on your commute, the answer is 0.6.
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?
To find the probability that you stop at neither of the traffic lights on your commute, we can use the complement rule.
The complement of stopping at neither traffic light is not stopping at neither traffic light, which means stopping at one or both traffic lights.
Using the information provided, we can calculate the probability of stopping at one or both traffic lights as follows:
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, the probability of not stopping at one or both traffic lights is the complement of stopping at one or both traffic lights. We can calculate it as:
P(not A∪B) = 1 - P(A∪B)
P(not A∪B) = 1 - 0.6
P(not A∪B) = 0.4
Hence, the probability that you stop at neither of the traffic lights on your commute is 0.4.
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 but not the second, we can use the formula:
P(A∩not B) = P(A) - P(A∩B)
Given that the probability of stopping at the first traffic light (event A) is 0.4, and the probability of stopping at both traffic lights (A∩B) is 0.3, we can substitute the values into the formula:
P(A∩not B) = 0.4 - 0.3
P(A∩not B) = 0.1
Therefore, the probability that you stop at the first traffic light but not the second is 0.1.
To find the probability of stopping at one or more traffic lights on your commute, you can use the principle of inclusion-exclusion.
First, let's compute the probability of stopping at the first traffic light (A) only. This is given by P(A) - P(A∩B), which is 0.4 - 0.3 = 0.1.
Similarly, let's compute the probability of stopping at the second traffic light (B) only. This is given by P(B) - P(A∩B), which is 0.5 - 0.3 = 0.2.
Next, let's compute the probability of stopping at both traffic lights (A∩B). This is already given as 0.3.
To find the probability of stopping at one or more traffic lights, we need to add the probabilities of the individual events (A only, B only) and the intersection (A∩B):
P(stop at one or more traffic lights) = P(A only) + P(B only) + P(A∩B)
= 0.1 + 0.2 + 0.3
= 0.6
Therefore, the probability that you stop at one or more traffic lights on your commute is 0.6 or 60%.
To find the probability that you stop at one or more traffic lights on your commute, we can use the principle of inclusion-exclusion.
First, let's calculate the probability of stopping at either the first or the second traffic light individually.
The probability of stopping at the first traffic light (A) is given as 0.4.
The probability of stopping at the second traffic light (B) is given as 0.5.
Next, we need to calculate the probability of stopping at both traffic lights (A∩B), which is given as 0.3.
To find the probability of stopping at one or more traffic lights, we can add the probabilities of stopping at the first traffic light and the second traffic light, and then subtract the probability of stopping at both traffic lights because it was counted twice.
P(A∪B) = P(A) + P(B) - P(A∩B)
P(A∪B) = 0.4 + 0.5 - 0.3
P(A∪B) = 0.6
Therefore, the probability that you will stop at one or more traffic lights on your commute is 0.6, or 60%.