Question

"It was a 20% chance of rain between noon and 1pm and there is a 60% chance that the dog walker may come at that time. What percentage that the dog walker will be walking in the rain with the dogs?"

please help me with this.
I know both events are independent but I'm not sure if this is the way to solve it:

20% = 1/5
60% = 3/5
1/5*3/5= 3/25 which is 12% that both events occur at the same time

is it correct?
if not... how can I practice this? is it compound probability?
Thank you very much! ​

Answer 1

To find the probability that both events will occur at the same time, you need to use the formula for the probability of the intersection of two events. In this case, the probability that it will rain between noon and 1pm AND that the dog walker will come at that time is:

P(Rain AND Dog Walker) = P(Rain) * P(Dog Walker | Rain)

The probability that it will rain is 20%, or 1/5. The probability that the dog walker will come at that time given that it is raining is 60%, or 3/5. Plugging these values into the formula above, we get:

P(Rain AND Dog Walker) = (1/5) * (3/5) = 3/25 = 12%

So the probability that the dog walker will be walking in the rain with the dogs is 12%.

To practice solving problems like this, you can try solving similar problems where you are given different probabilities for the two events. This will help you become more comfortable with using the formula for the probability of the intersection of two events.

Explanation: