Question

(a) If a die is thrown three times, find the probability of getting one appearing number in them will be odd:

Hint:

Use the binomial theorem for probabilities involving repeated independent trials.

Answer 1

For a die, the numbers that are odd are \( 1, 3, 5 \). The probability of rolling an odd number is: \[ P(\text{odd}) = \frac{3}{6} = \frac{1}{2}. \] The probability of rolling an even number is also \( \frac{1}{2} \). Using the binomial probability formula, for exactly one odd number in three rolls: \[ P(\text{one odd}) = \binom{3}{1} \left( \frac{1}{2} \right)^1 \left( \frac{1}{2} \right)^2 = 3 \cdot \frac{1}{8} = \frac{3}{8}. \]