Question: 4. A ten sided die is numbered from one to ten. What is the probability of rolling a four on 3…

4. A ten sided die is numbered from one to ten. What is the probability of rolling a four on 3 consecutive rolls? (3 marks)

Solution

Step 1: The probability of rolling a 4 on a single roll is: \[ \frac{1}{10} \] Step 2: Since each roll is independent, the probability of rolling a 4 three times in a row is: \[ \left( \frac{1}{10} \right)^3 = \frac{1}{1000} \] The probability of rolling a four on 3 consecutive rolls is \(\frac{1}{1000}\).