Question

One hundred identical coins, each with probability p of showing up heads are tossed once. If 0 < p < 1 & the probability of heads showing on fifty coins is equal to that of heads showing on 51 coins, then the value of p is :

• A. 1/2
• B. 49/101
• C. 50/101
• D. 51/101

Answer 1

Answer: (D)

Probability of 50 coins showing up heads = Probability of 51 coins showing up heads
$\Rightarrow {}^{100}{C}_{50}{p}^{50}(1-p{)}^{50}={}^{100}{C}_{51}{p}^{51}(1-p{)}^{49}$
$\Rightarrow p=\frac{51}{101}$