Question

The probability of obtaining at least one head when we toss n unbiased coins is

• A. $\frac{C_0^n}{2^n}$
• B. $\frac{1-C_r^n}{2^n}$
• C. $1-\frac{1}{2^n}$
• D. $\frac{C_r^n}{2^n}$

Answer 1

Answer: (C)

$1-\frac{1}{2^n}$

P(at least $1$ head) $=1-$ P(all tails)
Now P(all tails) $=$ P(tails in $1$st toss) $\times$ P(tails in $2$nd toss) $\times$ P(tails in $3$rd toss) .... $\times$ P(tails in $n$th toss)
$=\frac{1}{2}$ x $\frac{1}{2}$ x $\frac{1}{2}$ x .......$\frac{1}{2}$ (upto $n$ terms)
$=\frac{1}{2^n}$
So, P(at least $1$ head) $=1-\frac{1}{2^n}$