# One Hundred Identical Coins, Each with Probability P of Showing Heads Are Tossed Once. If 0 < P < 1 and the Probability of Heads Showing on 50 Coins is Equal to that of Heads Showing on 51 Coins - Mathematics

MCQ

One hundred identical coins, each with probability p of showing heads are tossed once. If 0 < p < 1 and the probability of heads showing on 50 coins is equal to that of heads showing on 51 coins, the value of p is

#### Options

• 1/2

• 51/101

• 49/101

• None of these

#### Solution

51/101

$\text{ Let X denote the number of coins showing head .}$
$\text{ Therefore, X follows a binomial distribution with p and n as parameters . }$
$\text{ Given that } P(X = 50) = P(X = 51)$
$\Rightarrow ^{100}{}{C}_{50} \ p^{50} q^{50} = ^{100}{}{C}_{51} \ p^{51}\ q^{49}$
$\text{ on simplifying we get } ,$
$\frac{51}{50} = \frac{p}{q}$
$\Rightarrow \frac{51}{50} = \frac{p}{1 - p} (\text{ since} \ p + q = 1)$
$\Rightarrow p = \frac{51}{101}$

Concept: Bernoulli Trials and Binomial Distribution
Is there an error in this question or solution?

#### APPEARS IN

RD Sharma Class 12 Maths
Chapter 33 Binomial Distribution
MCQ | Q 9 | Page 28