Question

Two players toss 4 coins each. The probability that they both obtain the same number of heads is

• A. $\frac{5}{256}$
• B. $\frac{1}{16}$
• C. $\frac{35}{126}$
• D. $\frac{3}{16}$

Answer 1

The correct option is C $\frac{35}{126}$

Required probability = P(0 head) + P(1 head) + P(2 heads) + P(3heads) + P(4 heads)
$={\left\{4C_0{\left(\frac{1}{2}\right)}^0{\left(\frac{1}{2}\right)}^4\right\}}^2+{\left\{4C_1{\left(\frac{1}{2}\right)}^1{\left(\frac{1}{2}\right)}^3\right\}}^2+{\left\{4C_2{\left(\frac{1}{2}\right)}^2{\left(\frac{1}{2}\right)}^2\right\}}^2+{\left\{4C_3{\left(\frac{1}{2}\right)}^3{\left(\frac{1}{2}\right)}^1\right\}}^2+{\left\{4C_4{\left(\frac{1}{2}\right)}^4{\left(\frac{1}{2}\right)}^0\right\}}^2$
$=\frac{70}{256}=\frac{35}{128}$