Question

Suppose P(A)=0.55, P(B)=0.45, P(A∪B')=0.7.

Find P(A∪B). Enter your answer to 3 decimal places.

Answer 1

We know,

$P(A\cup B) = P(A) + P(B) - P(A\cap B)$------------------ 1

but,

$P(A\cup B{}') = P(A) + P(B{}') - P(A\cap B{}')$--------------------------2

but

$P(A\cap B{}') = P(A) - P(A\cap B)$----------------------3

So therefore put equation 3 in equation 2, We get

$P(A\cup B{}') = P(A) + P(B{}') - P(A) + P(A\cap B)}$

$P(A\cup B{}') = P(B{}') + P(A\cap B)$

but $P(B{}') = 1-P(B)$

We get

$P(A\cup B{}') = 1 - P(B) + P(A\cap B)$

So therefore $P(A\cap B) = P(A\cup B{}') - 1 + P(B)$

We get $P(A\cap B) = 0.7 - 1 + 0.45 = 0.15$

So therefore Equation 1 becomes

$P(A\cup B) = P(A) + P(B) - P(A\cap B)$

$P(A\cup B) = 0.55 + 0.45 - 0.15 = 0.850$

$P(A\cup B) = 0.850$