Mutually exclusive or not? Mutually exclusive. Probability: 29 or about 22.2 %
Practice makes perfect
We want to determine whether the events are mutually exclusive and find the probability of their intersection. 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 roll a pair of dice at the same time.
Let A be getting a sum of 6 and B be getting a sum of 10.
A sum rolled on a pair of dice cannot be both 6 and 10 at the same time. Therefore, A and B are mutually exclusive events.
Probability
Now, we can find the probability that we get a sum of 6 or a sum of 10 on a pair of dice.
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 can calculate the number of total outcomes, which is also the number of times the experiment is done, for a pair of dice knowing that each die has 6 different outcomes.
6*6= 36 ← Total outcomes
Out of 36 times the experiment is done, a sum of six occurs 5 times and a sum of ten occurs 3 times. Now, we can calculate P(A) and P(B).
P(A)&=5/36 l← ← lSum of6 Total outcomes [0.5em]
P(B)&=3/36 l← ← lSum of10 Total outcomes
Finally, considering that A and B are mutually exclusive events, let's calculate P(AorB).
