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Events $A$A​ and $B$B​ are disjoint. Find $P\left(A\ \text{or}\ B\right)$P(A or B)​ when $P(A)=\frac{2}{3}$P(A)=23​​ and $P\left(B\right)=\frac{1}{5}$P(B)=15​​ .  Express your answer as a fraction in simplest form.$P\left(A\ \text{or}\ B\right)=$P(A or B)=​

Question

Events AAA​ and BBB​ are disjoint. Find P(A or B)P\left(A\ \text{or}\ B\right)P(A or B)​ when P(A)=23P(A)=\frac{2}{3}P(A)=23​​ and P(B)=15P\left(B\right)=\frac{1}{5}P(B)=15​​ .  Express your answer as a fraction in simplest form.P(A or B)=P\left(A\ \text{or}\ B\right)=P(A or B)=​

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Solution

The events A and B are disjoint, which means they cannot both occur at the same time. Therefore, the probability of either A or B occurring is simply the sum of their individual probabilities.

So, we have:

P(A or B) = P(A) + P(B)

Substituting the given values:

P(A or B) = 2/3 + 1/5

To add these fractions, we need a common denominator. The least common multiple of 3 and 5 is 15, so we convert each fraction to have this denominator:

P(A or B) = 10/15 + 3/15

Adding these fractions gives:

P(A or B) = 13/15

So, the probability of either event A or event B occurring is 13/15.

This problem has been solved

Similar Questions

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