If a fair coin is tossed 10 times, then the probability of getting all heads or all tails, is:
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → \(\displaystyle\frac{1}{2^{9}}\)
Ten tosses of a fair coin have \(2^{10}\) equally likely outcomes. Exactly one of them is all heads and exactly one is all tails, and these two events are mutually exclusive, so their probabilities add:
\( \displaystyle P(\text{all heads or all tails}) = \frac{1}{2^{10}} + \frac{1}{2^{10}} \)
\( \displaystyle = \frac{2}{2^{10}} = \frac{1}{2^{9}} \)