Three unbiased coins are tossed. What is the probability of getting at least 2 heads? Option 1: 1/8 Option 2: 1/4 Option 3: 1/2 Option 4: 1/3

Answer: 1/2. Solution: "At least 2 heads" means 2 heads OR 3 heads. When tossing 3 coins, each coin can land in 2 ways: Heads (H) or Tails (T). Total possible outcomes = 2 x 2 x 2 = 8 All 8 possible outcomes: 1. HHH (3 heads) 2. HHT (2 heads) 3. HTH (2 heads) 4. HTT (1 head) 5. THH (2 heads) 6. THT (1 head) 7. TTH (1 head) 8. TTT (0 heads) Outcomes with 2 heads OR 3 heads: Exactly 3 heads: HHH → 1 outcome Exactly 2 heads: HHT, HTH, THH → 3 outcomes Total favorable outcomes = 1 + 3 = 4 Probability = (Number of favorable outcomes)/(Total number of outcomes) Probability = 4/8 Probability = 1/2 Therefore, the probability of getting at least 2 heads is 1/2.

Quantitative Reasoning

Probability

Easy

Three unbiased coins are tossed. What is the probability of getting at least 2 heads?

$\frac{1}{8}$

$\frac{1}{4}$

$\frac{1}{2}$

$\frac{1}{3}$

✅ Correct Option: 3

"At least 2 heads" means 2 heads OR 3 heads.

When tossing 3 coins, each coin can land in 2 ways: Heads (H) or Tails (T).

Total possible outcomes $= 2 \times 2 \times 2 = 8$

All 8 possible outcomes:

HHH (3 heads)
HHT (2 heads)
HTH (2 heads)
HTT (1 head)
THH (2 heads)
THT (1 head)
TTH (1 head)
TTT (0 heads)

Outcomes with 2 heads OR 3 heads:

Exactly 3 heads: HHH → 1 outcome

Exactly 2 heads: HHT, HTH, THH → 3 outcomes

Total favorable outcomes $= 1 + 3 = 4$

Probability $= \dfrac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}$

Probability $= \dfrac{4}{8}$

Probability $= \dfrac{1}{2}$

Therefore, the probability of getting at least 2 heads is $\dfrac{1}{2}$ .

2026: 29 May Shift 1

Consider the experiment of rolling a die. Let A be the event 'getting a prime number', B be the event 'getting an odd number'. However C be the event containing only highest number of die. If P is the probability of the events.

(A) Here, $S = \{1,2,3,4,5,6\}, A = \{2,3,5\}, B = \{1,3,5\}, C = \{6\}$

(B) $A \cup B = \{1,2,3,5\}$ & $A \cap B = \{3,5\}$

(D) $P(A \cup B) = P(A) + P(B) - P(A \cap B)$

Arrange the above events in chronological order and choose the correct answer from the options given below:

2025: 3 June Shift 2

A basket contains 4 red, 5 blue and 3 green marbles. If three marbles are picked up at random, what is the probability that at least one is blue?

2026: 24 May Shift 1

If a dice is thrown, what is the probability of getting 6 ?

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?

2023: 5 June Shift 2

A and B are mutually exclusive events. The probability of occurrence of A is $\frac{3}{5}$ and the probability of occurrence of B as $\frac{1}{3}$ . What is the probability of both A and B occurring at the same time?

Three unbiased coins are tossed. What is the probability of getting at least 2 heads?

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