Mutually exclusive or not? Mutually exclusive. Probability: 100 %
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.
Let A be getting heads and B be getting tails on a coin.
The coin can only land on one side, so we cannot get both heads and tails. Therefore, A and B are mutually exclusive events.
Probability
Now, we can find the probability that the coin lands on either heads or tails.
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).
We know that the coin has 2 sides. Out of these, there is 1 side called heads and 1 called tails.
Now, we can calculate P(A) and P(B).
P(A)&=1/2 l← ← lHeads Total sides
P(B)&=1/2 l← ← lTails Total sides
Finally, considering that A and B are mutually exclusive events, let's calculate P(AorB).
