Respuesta :
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:
[tex]A = a + (A \cap B)[/tex]
In which a is the probability that A occurs but B does not and [tex]A \cap B[/tex] is the probability that both A and B occur.
By the same logic, we have that:
[tex]B = b + (A \cap B)[/tex]
The probability that both A and B occur is 0.15.
This means that [tex]A \cap B = 0.15[/tex]
The probabilities of the events A and B are 0.20 and 0.30, respectively.
[tex]A = 0.20[/tex].
[tex]A = a + (A \cap B)[/tex]
[tex]0.20 = a + 0.15[/tex]
[tex]a = 0.05[/tex]
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[tex]B = 0.30[/tex]
[tex]B = b + (A \cap B)[/tex]
[tex]0.30 = b + 0.15[/tex]
[tex]b = 0.15[/tex]
What is the probability of either A or B occurring?
[tex]A \cup B = a + b + A \cap B = 0.05 + 0.15 + 0.15 = 0.35[/tex]
35% probability of either A or B occurring
