JAMIA 2024 — Mathematics PYQ

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Question

JAMIA 2024 — Mathematics PYQ

JAMIA | Mathematics | 2024

If $P (A) = 0.4, P (B) = 0.7$ and $P (B ∣ A) = 0.6$ then $P (A \cup B)$ is equal to

Choose the correct answer:

Explanation

Step 1: Given Information

We are given:

$P(A) = 0.4$
$P(B) = 0.7$
$P(B|A) = 0.6$

Step 2: Find the Intersection $P(A \cap B)$

Using the definition of Conditional Probability:

P(B|A) = \frac{P(A \cap B)}{P(A)}

Rearranging the formula to find $P(A \cap B)$ :

P(A \cap B) = P(B|A) \cdot P(A)

P(A \cap B) = 0.6 \cdot 0.4 = 0.24

Step 3: Apply the Addition Rule

The formula for the probability of the union of two events is:

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

Substitute the values we have:

P(A \cup B) = 0.4 + 0.7 - 0.24

P(A \cup B) = 1.1 - 0.24

P(A \cup B) = 0.86

Final Answer

The value of $P(A \cup B)$ is:

0.86