A die is rolled thrice. What is the probability of getting a number greater than 4 in the first and the second throw of dice and a number less than 4 in the third throw?
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → \(\displaystyle\frac{1}{18}\)
A number greater than 4 is 5 or 6, and a number less than 4 is 1, 2 or 3:
\( \displaystyle P(\text{greater than } 4) = \frac{2}{6} = \frac{1}{3} \)
\( \displaystyle P(\text{less than } 4) = \frac{3}{6} = \frac{1}{2} \)
The three throws are independent, so the probabilities multiply:
\( \displaystyle P = \frac{1}{3}\times\frac{1}{3}\times\frac{1}{2} = \frac{1}{18} \)