Question

Given P(A)=0.4P(A)=0.4, P(B)=0.26P(B)=0.26 and P(A\text{ or }B)=0.436P(A or B)=0.436, find the value of P(A\text{ and }B)P(A and B), rounding to the nearest thousandth, if necessary.

Answer 1

If the probabilities of A, B, and A or B are 0.4, 0.26, and 0.436. Then the probability of A and B will be 0.224.

What is the addition rule of size for two subsets?

For two subsets A and B of the universal set U, we have:

P(A ∪ B) = P(A) + P(B) - P(A ∩ B)

Then the expression can be written as

P(A ∩ B) = P(A) + P(B) - P(A ∪ B)

The probabilities are given below.

P(A) = 0.4

P(B)=0.26

P(A ∪ B) = 0.436

Then the probability of A and B will be

P(A ∩ B) = P(A) + P(B) - P(A ∪ B)

P(A ∩ B) = 0.4 + 0.26 - 0.436

P(A ∩ B) = 0.66 - 0.436

P(A ∩ B) = 0.224

Learn more about the addition rule for two subsets here:

https://brainly.com/question/27496136

SPJ1