Answer:
C. [tex]P(B) =0.45[/tex]
Step-by-step explanation:
We have been given that the probability that event A occurs is 0.4, and the probability that events A and B both occur is 0.25. The probability that either event A or event B occurs is 0.6. We are asked to find the probability that event B will occur.
We have been given[tex]P(A) = 0.4[/tex], [tex]P(A\cap B) = 0.25[/tex] and [tex]P(A\cup B) = 0.6[/tex].
We will use the formula [tex]P(A)+P(B) =P(A\cup B)+P(A\cap B)[/tex].
Upon substituting our given values in above formula, we will get:
[tex]0.4+P(B) =0.60+0.25[/tex]
[tex]0.4+P(B) =0.85[/tex]
[tex]0.4-0.4+P(B) =0.85-0.4[/tex]
[tex]P(B) =0.45[/tex]
Therefore, the probability that event B will occur is 0.45 and option C is the correct choice.
