Question

An unbiased coin is tossed six times. The probability of obtaining at least one head and at least one tail is?

1. \(\rm \frac{1}{31}\)
2. \(\rm \frac{31}{32}\)
3. \(\rm \frac{32}{31}\)
4. \(\rm \frac{1}{32}\)

Answer 1

Correct Answer - Option 2 : \(\rm \frac{31}{32}\)

Calculation:

Required probability = 1 - [P(No head) + P(No Tail)]

= 1 -  \(\rm \left \{ \frac{1}{2^{6}} + \frac{1}{2^{6}} \right \}\)  

=  1 - \(\rm \frac{1}{2^{5}}\)

Required probability =  \(\rm 1 - \frac{1}{32}\) = \(\rm \frac{31}{32}\)

The probability of obtaining at least one head and at least one tail is \(\rm \frac{31}{32}\)