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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 $P(A)=0.3$P(A)=0.3​ and $P\left(B\right)=0.1$P(B)=0.1​ .$P\left(A\ \text{or}\ B\right)=$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)=0.3P(A)=0.3P(A)=0.3​ and P(B)=0.1P\left(B\right)=0.1P(B)=0.1​ .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) = 0.3 + 0.1 = 0.4

So, the probability of either event A or event B occurring is 0.4.

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