There is a 10% it will rain on both Saturday and Sunday. There is a 25% chance of rain
on Saturday. What is the chance of rain on Sunday?
To find the chance of rain on Sunday, we can use conditional probability.
Conditional probability is the probability that an event will occur given that another event has already occurred. In this case, we want to find the probability of rain on Sunday given that it will rain on both Saturday and Sunday.
The probability of rain on both Saturday and Sunday can be calculated by multiplying the individual probabilities of rain on those days. So, the probability of rain on both Saturday and Sunday is 10% or 0.10.
Now, we know that the probability of rain on Saturday is 25% or 0.25. Since rain on both days is mutually inclusive, we can use conditional probability to find the probability of rain on Sunday.
The conditional probability formula is:
P(A|B) = P(A and B) / P(B)
Where:
P(A|B) is the probability of event A occurring given that event B has occurred.
P(A and B) is the probability of both events A and B occurring, which in this case is the probability of rain on both Saturday and Sunday (0.10).
P(B) is the probability of event B occurring, which in this case is the probability of rain on Saturday (0.25).
Applying the formula, we can find the probability of rain on Sunday:
P(rain on Sunday | rain on Saturday) = 0.10 / 0.25 = 0.40
Therefore, there is a 40% chance of rain on Sunday.