Let x denotes the number of heads in a simultaneous toss of three coins, then \(P(0 \lt x \le 3)\)
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → \(\displaystyle\frac{7}{8}\)
Three coins give \(2^3 = 8\) equally likely outcomes, and x takes the values 0, 1, 2, 3. So \(0 \lt x \le 3\) means “at least one head”, the complement of x = 0 (all tails):
\( \displaystyle P(x = 0) = P(\text{TTT}) = \frac{1}{8} \)
\( \displaystyle P(0 \lt x \le 3) = 1 - \frac{1}{8} = \frac{7}{8} \)