Quantitative Reasoning

Probability

Medium

If A and B are mutually exclusive events, then following probability of the events are given below:

(A) P(A) =0.4, P(B) =0.4 and P(AUB)=0.8

(B) P(A) =0.3, P(B) =0.6 and P(AUB)=0.9

(C) P(A) =0.3, P(B) =0.3 and P(AUB)=0.6

(D) P(A) =0.1, P(B) =0.1 and P(AUB)=0.2

which of the following options is correct?

(A), (B) and (D) only

(B) and (C) only

(A), (B), (C) and (D)

(D) and (A) only

✅ Correct Option: 3

For mutually exclusive events $P(A \cap B) = 0$ , so $P(A \cup B) = P(A) + P(B)$ .

Check each: $0.4+0.4=0.8$ , $0.3+0.6=0.9$ , $0.3+0.3=0.6$ , $0.1+0.1=0.2$ . All four satisfy the addition rule and every probability lies within $[0,1]$ , so all statements are consistent.

2023: 7 June Shift 1

Three coins are tossed once. Probability of getting no head is :

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:

2023: 15 June Shift 2

If $P(E) = 0.05$ , what is the probability of 'not E'?

2026: 20 May Shift 1

The probability that a card drawn from a pack of 52 cards will be a spade or a queen, is

2023: 15 June Shift 2

A bag contains 6 red, 4 blue and 10 white balls. A ball is picked from the bag at random. What is the probability that it is neither white nor blue?

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?

Solution

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