A dice is thrown twice, the probability of occurrence of 5 at least once is
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → \(\displaystyle\frac{11}{36}\)
“At least once” is easiest through the complement, “5 does not appear in either throw”. The two throws are independent:
\( \displaystyle P(\text{no 5 in both throws}) = \frac{5}{6} \times \frac{5}{6} = \frac{25}{36} \)
\( \displaystyle P(\text{5 at least once}) = 1 - \frac{25}{36} = \frac{11}{36} \)
Check by counting: the outcomes with a 5 are (5, 1) to (5, 6) and (1, 5) to (6, 5), that is \(6 + 6 - 1 = 11\) of the 36, since (5, 5) is counted twice.