Algebra

Probability

Medium

core

If A and B are two events such that P(A) ≠ 0 and P(B | A) = 1 then

$A \subset B$

$B \subset A$

$B = \phi$

$A = \phi$

✅ Correct Option: 1

Given information:

$P(A) \neq 0$ (Event A is not impossible)
$P(B | A) = 1$ (If A happens, then B happens with certainty)

When $P(B | A) = 1$ , it means that whenever A occurs, B must also occur.

The conditional probability formula:

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

Substituting $P(B | A) = 1$ :

$1 = \frac{P(A \cap B)}{P(A)}$

$P(A \cap B) = P(A)$

The equation $P(A \cap B) = P(A)$ means that whenever A happens, both A and B happen together.

In set notation, this means all elements of A are also in B.

Therefore: $A \subset B$ (A is a subset of B)

Why other options are incorrect:

$B \subset A$ : This would mean B is a subset of A, contradicting the established relationship.

$B = \phi$ : If B were empty, $P(B | A)$ could not equal 1.

$A = \phi$ : This contradicts the given condition $P(A) \neq 0$ .

The answer is: $A \subset B$

2022: 17 Aug Shift 2

If $A$ and $B$ are independent events such that $0 < P(A) < 1$ and $0 < P(B) < 1$ , then identify the correct statements.

(A) $A$ and $B'$ are independent

(B) $A'$ and $B$ are independent

(D) $A'$ and $B'$ are independent

Choose the correct answer from the options given below :

2022: 17 Aug Shift 2

It is given that only 0.1% of a large population have COVID infection. In this population, the reliability of COVID RTPCR-test is specified as follows :

For persons having COVID, 90% of the test detects the disease but 10% goes undetected. For persons not having COVID, 99% of the test is judged COVID negative but 1% are diagnosed as COVID positive.

Based on the above informations, answer the question :

The probability that randomly selected person from a population, not having COVID is :

2025: 13 May Shift 2

In a box containing 100 bulbs, 10 are defective. The probability that out of a sample of 5 bulbs, none is defective is

2026: 14 May Shift 2

A bag contains 5 white, 4 black and 3 red balls. Which of the following statements are True?

A. The probability of drawing three red balls one by one without replacement is $\frac{1}{220}$

B. One by one three balls drawn without replacement then probability that third ball is red is $\frac{1}{4}$

C. The probability of drawing 2 white balls one by one without replacement is $\frac{3}{4}$

D. One by one 3 balls are drawn without replacement then probability that third ball is red is $\frac{3}{4}$

Choose the correct answer from the options given below:

2026: 19 May Shift 1

Match List-I with List-II

List-I	List-II
(A) $P(A \cap B) = P(A).P(B)$	(I) $\frac{P(B \cap A)}{P(A)}, P(A) \ne 0$
(B) $\frac{P(S \cap B)}{P(B)}$ , S = Sample space	(II) A, B are independent events
(C) $P(B/A) =$	(III) $P(\bar{A} \cap \bar{B})$
(D) $P(\overline{A \cup B})$	(IV) 1

Choose the correct answer from the options given below:

2025: 15 May Shift 1

The probability of a man hitting a target is 1/2. How many times must he fire so that the probability of hitting the target at least once is more than 90%?

If A and B are two events such that P(A) ≠ 0 and P(B | A) = 1 then

Solution

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