Question

If a fair coin is tossed 20 times and let we get head n times, then probability that 21 is odd, is

• A. $\frac{1}{2}$
• B. $\frac{1}{6}$
• C. $\frac{5}{8}$
• D. $\frac{7}{8}$

Answer 1

Answer: (A)

Probability of getting head in one trial,
$p=1/2$ and probability of not getting head,
$q=1/2$ Probability of getting head odd times
${=}^{20}{C}_1{\left(\frac{1}{2}\right)}^1{\left(\frac{1}{2}\right)}^{19}{+}^{20}{C}_3{\left(\frac{1}{2}\right)}^3{\left(\frac{1}{2}\right)}^{17}$
$+....{+}^{20}{C}_{19}{\left(\frac{1}{2}\right)}^{19}{\left(\frac{1}{2}\right)}^1$
$=\frac{1}{2^{20}}{[}^{20}{C}_1{+}^{20}{C}_3+...{+}^{20}{C}_{19}]$
$=\frac{1}{2^{20}}\times 2^{20-1}\frac{2^{19}}{2^{20}}=\frac{1}{2}$