In a mountain village it rains on average 5 days a week. Find the probability that over a weekend it rains on exactly one of the two days.
If one considers each day independent of the day before (it is not),
pr(rainanyday)=5/7
Pr(rainonly one day)= 5/7 * 2/7 * 2ways
what can it happen on the weekend?
RR
RN
NR
NN
so of the possibilities, RN or nR are what we focus on.
Pr(rain only one day)=20/49
Lets check
Pr(rain both days)=25/49
pr(rain no days)=4/49
check: do these add to 1?
To find the probability that it rains on exactly one of the two days over the weekend, we need to consider the number of ways it can rain on exactly one day and divide it by the total number of possible outcomes.
First, let's determine the number of ways it can rain on exactly one day. Since it rains on average 5 days a week, the number of ways it can rain on one day over a weekend is (5 choose 1) * (2 choose 1) = 10. This is because there are 5 ways to choose a day when it rains, and 2 ways to choose which day of the weekend it will rain.
Next, let's calculate the total number of possible outcomes. Since there are 2 days over the weekend, each day can either have rain or not have rain, resulting in 2^2 = 4 possible outcomes.
Finally, we can find the probability by dividing the number of favorable outcomes (rain on exactly one day) by the total number of outcomes. Therefore, the probability is 10/4 = 2.5 or 50%.
So, the probability that over a weekend it rains on exactly one of the two days is 50%.