Question

A coin is tossed 2n times. The chance that the number of times one gets head is not equal to the number of times one gets tail is ______.

Options

• `(2"n"!)/("n"!)^2 (1/2)^("2n")`

• `1 - (2"n"!)/("n"!)^2`

• `1 - (2"n"!)/("n"!)^2 * 1/4^"n"`

• None of these

Answer 1

A coin is tossed 2n times. The chance that the number of times one gets head is not equal to the number of times one gets tail is `underline(1 - (2"n"!)/("n"!)^2 * 1/4^"n")`.

Explanation:

Probability of getting head is p = `1/2`

∴ q = `1 - 1/2 = 1/2`

The required probability

= 1 - Probability of equal number of heads and tails

= 1 - P(X = n)

`= 1 - "^(2n)C_n` `(1/2)^"n" (1/2)^(2"n" - "n")`

`= 1 - (2"n"!)/("n"!)^2 (1/2)^(2"n")`

`= 1 - (2"n"!)/("n"!)^2 xx 1/4^"n"`