Question

three coworkers are independently going to an event. two of them are late with probability 1/2, but one is only late with probability 1/3. what is the probability that exactly two people are late to the event

Answer 1

To find the probability that exactly two coworkers are late to an event, we consider the possible combinations where two can be late and calculate the probability for each, adding them up to get the total probability, which is 1/4.

Step-by-step explanation:

The question asks for the probability that exactly two coworkers are late to an event, given that two have a 1/2 chance of being late and one has a 1/3 chance. To solve this, we need to consider all the scenarios where exactly two coworkers can be late. These scenarios are:

1. The first two coworkers are late, and the third is not.
2. The first and the third coworkers are late, and the second is not.
3. The second and the third coworkers are late, and the first is not.

We calculate the probability of each scenario and then add them up to get the total probability for exactly two people being late.

For scenario 1, the probability is (1/2) * (1/2) * (2/3) = 1/6. For scenario 2, it is (1/2) * (1/2) * (1/3) = 1/12. For scenario 3, it is (1/2) * (2/3) * (1/2) = 1/6. Adding all these probabilities together, we get 1/6 + 1/12 + 1/6 = 1/4.

Therefore, the probability that exactly two people are late to the event is 1/4.