One hundred idential coins, each with probability p of showing heads are tossed once. If 0 < p

Q: One hundred idential 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:

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

M.C.Q (1 Marks)

GSEB - English Medium

One hundred idential 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:

A$\frac{1}{2}$
B$\frac{51}{101}$
C$\frac{49}{101}$
D$\text{None of these}$

STD 12 Science
Maths
Probability
Exemplar

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