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If A and B are events such that P(A) = 0.2, P(B) = 0.4 and P(A U B) = 0.5, then value of P(A/B) is
An event is a specific outcome or a set of outcomes of a random experiment. Events can be independent or dependent mutually exclusive or non-mutually exclusive. The probability of an event occurring is measured between 0 and 1 where 0 means impossible and 1 means certain occurrence.
Class 12 Maths Probability is explained in Chapter 13 for the CBSE Exam 2024-25. It covers important concepts like random experiments independent and dependent events mutually exclusive and non-mutually exclusive events Bayes’ theorem and conditional probability. Understanding these topics helps in solving real-life problems and is essential for higher studies and competitive exams.
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Given:
P(A) = 0.2
P(B) = 0.4
P(A ∪ B) = 0.5
Using the formula:
P(A ∪ B) = P(A) + P(B) – P(A ∩ B)
Substituting the values:
0.5 = 0.2 + 0.4 – P(A ∩ B)
0.5 = 0.6 – P(A ∩ B)
P(A ∩ B) = 0.1
Now, using the conditional probability formula:
P(A | B) = P(A ∩ B) / P(B)
P(A | B) = 0.1 / 0.4
P(A | B) = 0.25
So the correct answer is 0.25
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