Video Transcript
The days in a certain month were classified into rainy days and clear days. Find the probability that a day is clear using the given diagram.
In the Venn diagram drawn, we’re given a circle representing the number of rainy days. The number inside the circle tells us that there were two rainy days in the month. The number outside the circle is 28. And since 28 plus two is equal to 30, there were 30 days in total in the month. We can therefore conclude that the probability that a day was rainy is equal to two out of 30. Since both the numerator and denominator are even, we can divide them both by two. The probability that a day is rainy is therefore equal to one out of 15 or one fifteenth.
In this question, we are asked to find the probability that a day is clear. And we know that the days were classified into two options: rainy days and clear days. This means that the probability that a day is clear is the same as the probability it is not rainy. If we want an event to not occur, this is known as the complement of the event. The complement of event 𝐴 is denoted 𝐴 bar or 𝐴 prime. And the probability of this is one minus the probability of 𝐴. This means that in our question, the probability that a day is not rainy is equal to one minus one fifteenth. This is equal to fourteen fifteenths.
The probability that a day in the given month is clear is therefore equal to fourteen fifteenths.
