Question

The expected value of the number of heads obtained when three fair coins are tossed simultaneously is _____

• A. $1$
• B. $1.5$
• C. $0$
• D. $2$

Answer 1

Answer: (B)

$1.5$

The number of fair coins are $3$.

The probability of getting $3$ heads is $\frac{1}{2}\times \frac{1}{2}\times \frac{1}{2}=\frac{1}{8}$

The probability of getting $2$ heads is $3\times \frac{1}{2}\times \frac{1}{2}\times \frac{1}{2}=\frac{3}{8}$

The probability of getting $1$ heads is $3\times \frac{1}{2}\times \frac{1}{2}\times \frac{1}{2}=\frac{3}{8}$

The expected value of the number of heads is $1\times \frac{3}{8}+2\times \frac{3}{8}+3\times \frac{1}{8}=\frac{12}{8}=1.5$