Let A𝐴 and B𝐵 are two events and P(A′)=0⋅3𝑃𝐴'=0·3, P(B)=0⋅4, P(A∩B′)=0⋅5𝑃𝐵=0·4, 𝑃𝐴∩𝐵'=0·5 then P(A∪B′)𝑃𝐴∪𝐵' is:
Question
Let A𝐴 and B𝐵 are two events and P(A′)=0⋅3, P(B)=0⋅4, P(A∩B′)=0⋅5 then P(A∪B′) is:
Solution
To find the probability of P(A∪B′), we can use the formula of the union of two events which is given by:
P(A∪B′) = P(A) + P(B′) - P(A∩B′)
We already have P(A∩B′) = 0.5.
However, we don't have P(A) and P(B′) directly, but we have P(A′) and P(B).
We know that P(A) = 1 - P(A′) and P(B′) = 1 - P(B).
Substituting the given values:
P(A) = 1 - P(A′) = 1 - 0.3 = 0.7 P(B′) = 1 - P(B) = 1 - 0.4 = 0.6
Now, we can substitute these values into the formula:
P(A∪B′) = P(A) + P(B′) - P(A∩B′) = 0.7 + 0.6 - 0.5 = 0.8
So, P(A∪B′) = 0.8.
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