Question

The probability of getting at least $2$ heads, when an unbiased coin is tossed 6 times is

• A. $\frac{63}{64}$
• B. $\frac{57}{64}$
• C. $\frac{7}{64}$
• D. $\frac{37}{64}$

Answer 1

The correct option is B $\frac{57}{64}$

Probability of getting at least $2$ heads $=$ $1$ $-$ Probability of getting at most $1$ head
There are two cases for getting at most $1$ head
Case 1: When all are tails: T T T T T T $=1$
Case 2: When $1$ head and $5$ tails: H T T T T T $=6$ (we could arrange H at $6$ different places)
Probability of getting at least $2$ heads $=1-\frac{1+6}{2^6}=1-\frac{7}{64}=\frac{57}{64}$