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 A and B are disjoint. Find P(A or B) when P(A)=23 and P(B)=15 . Express your answer as a fraction in simplest form.P(A or B)=
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.
Similar Questions
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