A population can be divided into two subgroups that occur with probabilities 60% and 40%, respectively. An event A occurs 30% of

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A population can be divided into two subgroups that occur with probabilities 60% and 40%, respectively. An event A occurs 30% of

the time in the first subgroup and 50% of the time in the second subgroup. What is the unconditional probability of the event A, regardless of which subgroup it comes from

Mathematics

1 answer:

avanturin [10] · Answer 1 · 2023-05-16T19:14:06+03:00

The unconditional probability of the event A, regardless of which subgroup it comes from is 38%

<h3>How to determine the probability?</h3>

Let the events be represented as:

A ⇒ The event A happening
B ⇒ First subgroup
C ⇒ Second subgroup

So, we have:

P(B) = 60%

P(C) = 40%

P(A | B) = 30%

P(A | C) = 50%

The probability is then calculated as:

P = P(A | B) * P(B) + P(A | C) * P(C)

Substitute known values

P = 30% * 60% + 50% * 40%

Evaluate the product

P = 38%

Hence, the probability is 38%