Quantitative Reasoning

Probability

Easy

If three unbiased coins are tossed simultaneously, then the probability of exactly two heads is:

$\frac{3}{8}$

$\frac{1}{2}$

$\frac{1}{4}$

$\frac{1}{8}$

✅ Correct Option: 1

Three unbiased coins means each coin has an equal chance of showing Heads (H) or Tails (T). We want to find the probability of getting exactly 2 heads when tossing 3 coins simultaneously.

When tossing 3 coins, all possible outcomes are:

HHH

HHT

HTH

HTT

THH

THT

TTH

TTT

Total possible outcomes = 8

Each coin has 2 options, so $2 \times 2 \times 2 = 8$

Outcomes with exactly 2 heads:

HHT (2 heads, 1 tail)

HTH (2 heads, 1 tail)

THH (2 heads, 1 tail)

Favorable outcomes = 3

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

Probability $= \dfrac{3}{8}$

Therefore, the probability of exactly two heads is $\dfrac{3}{8}$ .

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If A and B are two disjoint events then

A. A ∩ B = Φ

B. P ( A ∩ B ) = 0

C. P ( A ∪ B ) = P (A) + P (B)

D. P ( A ∩ B ) = 1

Choose the correct answer from the options given below:

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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?

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If three unbiased coins are tossed simultaneously, then the probability of exactly two heads is:

Solution

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