Mutually exclusive or not? Not mutually exclusive.
Probability: 1320 or 65 %
Practice makes perfect
We want to determine whether the events are mutually exclusive and find the probability of their union. We will do these things one at a time.
Mutually Exclusive
Events that cannot occur at the same time are mutually exclusive. Mutually exclusive events have no outcomes in common. For example, because it is not possible to toss a coin and obtain heads and tails at the same time, these two events are mutually exclusive.
Rules for Probability
If A and B are mutually exclusive events, the probability that A and B will occur is P(AandB)=0.
If A and B are not mutually exclusive events, the probability that A and B will occur is P(AandB)≠0.
We select a number at random from integers 1 to 20. Let A be selecting an even number and B be selecting a number divisible by 3.
Three out of the ten even numbers are divisible by 3, so it is possible to be both an even number and a number divisible by 3. Therefore, A and B are not mutually exclusive events.
Probability
Now, we can find the probability that we select an even number or a number divisible by 3.
Addition Rules for Probability
If A and B are mutually exclusive events, the probability that A or B will occur is P(AorB)=P(A)+P(B).
If A and B are not mutually exclusive events, the probability that A or B will occur is P(AorB)=P(A)+P(B)-P(AandB).
When we select a number from integers 1 to 20, there are 20 numbers to choose from. Out of these, there are 10 even numbers, 6 numbers divisible by three, and 3 even numbers divisible by three. Now, we can calculate P(A), P(B), and P(AandB).
P(A)&=10/20 l← ← l Even Total numbers [0.5em]
P(B)&=6/20 l← ← l Divisible by3 Total numbers [0.5em]
P(AandB)&=3/20 l← ← l Even number divisible by3 Total numbers
Finally, considering that A and B are not mutually exclusive events, let's calculate P(AorB).
