Question

The probabilities of the events A and B are 0.20 and 0.30, respectively. The probability that both A and B occur is 0.15. What is the probability of either A or B occurring

Answer 1

Answer:

35% probability of either A or B occurring

Step-by-step explanation:

We solve this problem building the Venn's diagram of these probabilities.

We have two events, A and B.

We have that:

$A = a + (A \cap B)$

In which a is the probability that A occurs but B does not and $A \cap B$ is the probability that both A and B occur.

By the same logic, we have that:

$B = b + (A \cap B)$

The probability that both A and B occur is 0.15.

This means that $A \cap B = 0.15$

The probabilities of the events A and B are 0.20 and 0.30, respectively.

$A = 0.20$.

$A = a + (A \cap B)$

$0.20 = a + 0.15$

$a = 0.05$

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$B = 0.30$

$B = b + (A \cap B)$

$0.30 = b + 0.15$

$b = 0.15$

What is the probability of either A or B occurring?

$A \cup B = a + b + A \cap B = 0.05 + 0.15 + 0.15 = 0.35$

35% probability of either A or B occurring