Two events E and F are independent. If P(E) = 0.3, P(E U F) = 0.5, then P(E/F) – P(F/E) equals
Two events E and F are independent if the occurrence of one does not affect the occurrence of the other. Mathematically, they are independent if P(E ∩ F) = P(E) × P(F). This relationship is fundamental in probability theory and is used to solve various real-world problems.
Class 12 Maths Probability is discussed in Chapter 13 for the CBSE Exam 2024-25. It covers concepts like random experiments sample space independent and dependent events mutually exclusive and non-mutually exclusive events conditional probability and Bayes’ theorem. These topics are essential for solving real-life problems and are important for competitive exams and higher studies.
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Given:
P(E) = 0.3
P(E ∪ F) = 0.5
Since E and F are independent events, we use the formula:
P(E ∪ F) = P(E) + P(F) – P(E ∩ F)
Given that E and F are independent:
P(E ∩ F) = P(E) × P(F)
Substitute the values:
0.5 = 0.3 + P(F) – (0.3 × P(F))
0.5 = 0.3 + P(F) – 0.3P(F)
0.2 = P(F) – 0.3P(F)
0.2 = 0.7P(F)
P(F) = 2/7
Now, conditional probability calculations:
P(E | F) = P(E ∩ F) / P(F)
= (0.3 × 2/7) ÷ (2/7)
= 0.3
P(F | E) = P(E ∩ F) / P(E)
= (0.3 × 2/7) ÷ 0.3
= 2/7
Now, computing the needed difference:
P(E | F) – P(F | E) = 0.3 – 2/7
= 3/10 – 2/7
By taking LCM (70):
= (21/70) – (20/70)
= 1/70
Hence, the correct answer is 1/70
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