Mutually exclusive or not? Not mutually exclusive.
Probability: 1036 or about 27.8 %
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 roll a pair of dice at the same time.
Let A be getting doubles and B be getting a sum of 8.
If we roll two fours on a pair of dice, we get doubles and a sum of 8. Therefore, A and B are not mutually exclusive events.
Probability
Now, we can find the probability that we roll doubles or a sum of 8 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 possible outcomes for a pair of dice knowing that each die has 6 different outcomes.
6*6= 36 ← Total outcomes
Out of 36 possible outcomes, there are 6 outcomes that result in doubles, 5 outcomes that result in a sum of 8, and only 1 outcome that results in both.
Next, we can calculate P(A), P(B), and P(AandB).
P(A)&=6/36 l← ← lDoubles Total outcomes [0.5em]
P(B)&=5/36 l← ← lSum of8 Total outcomes [0.5em]
P(AandB)&=1/36 l ← ← lDoubles and a sum of8 Total outcomes
Finally, considering that A and B are not mutually exclusive events, let's calculate P(AorB).
