A fair coin is tossed 4 times. Find the probability of getting exactly two heads.

medium 2 marks Class 10 · Mathematics · Probability

Answer

3/8

The correct answer is 3/8 — Hence $P (exactly 2 heads) = \frac{6}{16} = \frac{3}{8}$ .

Step-by-step solution

The total number of equally likely outcomes is $2^{4} = 16$ .
Exactly two heads can occur in $(2 4) = 6$ ways (choose the 2 positions of heads).
Each such outcome has probability $1/16$ .
Hence $P (exactly 2 heads) = \frac{6}{16} = \frac{3}{8}$ .

Common mistake: Using

2^{2}

instead of

2^{4}

for total outcomes

Concept tested: Binomial probability