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If P(A) = p and P(B) = q then , a. P(A/B) ≤ p/q b. P(A/B) ≥ p/q c. P(A/B) ≤ q/p d. None of these?
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If P(A) = p and P(B) = q then , a. P(A/B) ≤ p/q b. P(A/B) ≥ p/q c. P(A...
Solution:

Given, P(A) = p and P(B) = q

We need to find the relation between P(A/B) and p/q.

Definition:

P(A/B) = P(A ∩ B) / P(B)

Approach:

We can use the given information to find the relation between P(A ∩ B) and p/q.

We know that P(A ∩ B) = P(B) * P(A/B)

Substituting values, we get

P(A/B) = P(A ∩ B) / P(B) = (P(B) * P(A/B)) / P(B) = P(A/B)

Therefore,

P(A/B) = P(A ∩ B) / P(B) = P(B ∩ A) / P(B)

= P(B/A) * P(A) / P(B)

= P(B/A) * p/q (using P(A) = p and P(B) = q)

We can use this relation to find the answer.

Answer:

b. P(A/B) ≥ p/q

Explanation:

We know that P(B/A) ≤ 1 (probability of event B is less than or equal to 1, given event A has occurred).

Therefore,

P(A/B) = P(B/A) * p/q ≤ p/q

Multiplying both sides by q/p, we get

P(A/B) * q/p ≤ 1

Therefore,

P(A/B) ≤ q/p

But we also know that P(A/B) ≥ 0 (probability is always non-negative).

Therefore,

0 ≤ P(A/B) ≤ q/p

But since q/p > 1 (given that P(B) > P(A)), we have

P(A/B) ≥ p/q

Therefore, the correct answer is b.
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If P(A) = p and P(B) = q then , a. P(A/B) ≤ p/q b. P(A/B) ≥ p/q c. P(A...
Answer is a)
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If P(A) = p and P(B) = q then , a. P(A/B) ≤ p/q b. P(A/B) ≥ p/q c. P(A/B) ≤ q/p d. None of these?
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