SATHEE: Probability 3 Question 3

Probability 3 Question 3

3. Let $A$ and $B$ be two non-null events such that $A \subset B$ . Then, which of the following statements is always correct.

(2019 Main, 8 April I)

(a) $P (A / B) = P (B) - P (A)$

(b) $P (A / B) \geq P (A)$

(d) $P (A / B) = 1$

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Solution:

We know that, $P (A / B) = \frac{P (A \cap B)}{P (B)}$

[by the definition of conditional probability]

$\begin{array}{lc} ∵ & A \subset B \\ \Rightarrow & A \cap B = A \\ ∴ & P (A / B) = \frac{P (A)}{P (B)} \end{array}$

As we know that, $0 \leq P (B) \leq 1$

$\begin{array}{lll} ∴ & 1 & \leq \frac{1}{P (B)} < \infty \Rightarrow P (A) \leq \frac{P (A)}{P (B)} < \infty \\ \Rightarrow & \frac{P (A)}{P (B)} & \geq P (A) \end{array}$

Now, from Eqs (i) and (ii), we get

$P (A / B) \geq P (A)$

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Probability 3 Question 3

3. Let A and B be two non-null events such that A⊂B. Then, which of the following statements is always correct.

Solution:

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3. Let $A$ and $B$ be two non-null events such that $A \subset B$ . Then, which of the following statements is always correct.