We have the following information:
P(A)=0.25
P(A∪B)=0.65
P(B)=x
Since A and B are independent events, we know that P(A∪B)=P(A)+P(B)−P(A∩B).
Substituting the given values, we have:
0.65=0.25+x−P(A∩B)
Since A and B are independent, the probability of their intersection (P(A∩B)) is simply the product of their individual probabilities:
P(A∩B)=P(A)∗P(B)
Substituting the values again, we have:
0.65=0.25+x−0.25x
Simplifying the equation, we get:
0.65=0.25+x−0.25x
0.65−0.25=0.75x
0.4=0.75x
x=0.750.4
x=158
Therefore, the value of x is158. The correct option is (C) 158.