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4. Suppose the probability of event A is 0.23, the probability of the intersection of event A and event Bis 0.12, and
the probability of the union of event A and event B is 0.34. Find the probability of the complement of event B.
(A) 0.11
(B) 0.23
(C) 0.48
(D) 0.52
(E) 0.77

Respuesta :

MrRoyal

Answer:

[tex]P(B') = 0.77[/tex]

Step-by-step explanation:

Given

[tex]P(A) = 0.23[/tex]

[tex]P(A\ n\ B) = 0.12[/tex]

[tex]P(A\ u\ B) = 0.34[/tex]

Required

Find P(B')

First, we calculate P(B).

We have:

[tex]P(A\ n\ B) = P(A) + P(B) - P(A\ u\ B)[/tex]

Substitute values

[tex]0.12 = 0.23 + P(B) - 0.34[/tex]

[tex]0.12 = 0.23 - 0.34 + P(B)[/tex]

Collect like terms

[tex]P(B) = 0.12 - 0.23 + 0.34[/tex]

[tex]P(B) = 0.23[/tex]

P(B') is then calculated as:

[tex]P(B') = 1 - P(B)[/tex]

[tex]P(B') = 1 -0.23[/tex]

[tex]P(B') = 0.77[/tex]

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