The probability of rolling a 3 or 2 on a single die is an example of mutually exclusive events. True or False.
Mutually exclusive events are defined as events that cannot occur or happen at the same time. In other words, the probability of the events happening at the same time is zero.
Answer: The probability of rolling a 3 or 2 on a single die is 1/3 and an example of mutually exclusive events as we cannot roll 2 and 3 both at the same time.
Let us proceed step by step.
To explain the concept, let us first consider it as conditional probability.
As we know conditional probability is,
P(A | B) = P(A ∩ B) / P(B)
Where P(A | B) is the probability of event A where event B has already occurred.
But in this case, two events cannot occur simultaneously.
Hence it is an example of mutually exclusive events.
We can calculate it by
P (3 ∪ 2) = 1 /6 + 1 / 6 = 2 / 6
On further simplifying, we get
P (3 ∪ 2) = 1 / 3