A coin is tossed four times. The probability of getting at least 1 head before getting the first tail is
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → \( \displaystyle\frac{1}{2} \)
“At least 1 head before the first tail” means the sequence does not start with a tail, i.e. the first toss is a head. What happens on the later tosses does not matter.
\( \displaystyle P(\text{first toss is a head})=\frac{1}{2} \)
Why the other options are incorrect
Option (1) \( \displaystyle\frac{1}{2^4} \) — Incorrect. This is the probability of one particular sequence of four tosses, such as HHHH.
Option (3) \( 1-\displaystyle\frac{1}{2^4} \) — Incorrect. This is the probability of getting at least one head anywhere in the four tosses, which also counts sequences starting with a tail.
Option (4) \( \displaystyle\frac{3}{4} \) — Incorrect. The probability is \( \frac{1}{2} \), not \( \frac{3}{4} \).