Quantitative Reasoning

Probability

Medium

Match List-I with List-II

List-I List-II
(Statements/Expressions, etc.) (Value/Expressions, etc.)
(A) P(E) (I) 1
(B) The probability of an impossible event (II) P(A). P(B)
(C) For exhaustive events E₁ and E₂, P(E₁ ∪ E₂)= (III) 1-P(Ē)
(D) For independent events A and B, P(A ∩ B)= (IV) 0

Choose the correct answer from the options given below:

List-I	List-II
(Statements/Expressions, etc.)	(Value/Expressions, etc.)
(A) P(E)	(I) 1
(B) The probability of an impossible event	(II) P(A). P(B)
(C) For exhaustive events E₁ and E₂, P(E₁ ∪ E₂)=	(III) 1-P(Ē)
(D) For independent events A and B, P(A ∩ B)=	(IV) 0

(A) - (I), (B) - (II), (C) - (III), (D) - (IV)

(A) - (II), (B) - (III), (C) - (IV), (D) - (I)

(A) - (III), (B) - (IV), (C) - (I), (D) - (II)

(A) - (IV), (B) - (I), (C) - (II), (D) - (III)

✅ Correct Option: 3

For P(E), the relationship with its complement is:

$P(E) = 1 - P(\bar{E})$

where $\bar{E}$ represents the event that E does not happen.

The probability of an event equals 1 minus the probability of its complement.

Match: A → III

An impossible event is something that can never occur.

The probability of an impossible event is 0.

Example: Getting a 7 when rolling a standard dice (which only has faces 1-6).

Match: B → IV

Exhaustive events are events that cover all possible outcomes. At least one of them must happen.

For exhaustive events E₁ and E₂:

$P(E_1 \cup E_2) = 1$

Example: When flipping a coin, Heads and Tails are exhaustive events, so $P(\text{Heads} \cup \text{Tails}) = 1$ .

Match: C → I

Independent events are events where the occurrence of one does not affect the probability of the other.

For independent events A and B:

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

Example: Flipping a coin and rolling a dice are independent. $P(\text{Heads} \cap \text{getting 6}) = \frac{1}{2} \times \frac{1}{6} = \frac{1}{12}$

Match: D → II

Final matching:

(A) → (III)

(B) → (IV)

(D) → (II)

2025: 19 May Shift 1

A bag contains 4 red, 5 blue and 3 green balls. If two balls are drawn at random from the bag, then which of the following statements are correct?

(A) The probability that both balls are red is $\frac{1}{11}$ .

(B) The probability that one ball is red, and one ball is blue is $\frac{10}{33}$ .

(D) The probability that both balls are green is $\frac{5}{11}$ .

Choose the correct answer from the options given below:

2025: 29 May Shift 1

In a musical chair game, the person playing the music has been advised to stop playing the music at any time within 1.5 minutes after he starts playing. What is the probability that the music will stop within the first 15 seconds after starting?

2025: 26 May Shift 1

A speaks the truth in 70% of cases and B lies in 40% of cases. The probability that they will say the same thing while describing a single event (to have occurred or not) will be:

2025: 29 May Shift 2

A and B are participating in the same contest, the probability of their winning are $\frac{5}{8}$ and $\frac{1}{4}$ respectively. What is the probability that neither of them will win the contest?

2025: 22 May Shift 2

In a simultaneous throw of a pair of dice, what is the probability of getting a total more than 8?

2025: 15 May Shift 1

A bag contains 4 red, 5 blue and 3 green balls. If two balls are drawn at random from the bag, then which of the following statements are correct?

(A) The probability that both balls are red is 1/11.

(B) The probability that one ball is red, and one ball is blue is 10/33

(D) The probability that both balls are green is 5/11.

Choose the correct answer from the options given below:

Solution

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