Question

If a die is thrown three times, then find the probability of getting at least one odd number.

Hint:

Use the complement: 1 - P(all three throws are even).

Answer 1

Step 1: Find the probability of NOT getting an odd number on a single throw:
A die has 3 odd faces (1,3,5) and 3 even faces (2,4,6), so \(P(\text{even})=\dfrac36=\dfrac12\).

Step 2: Find the probability of getting NO odd number in all three throws:
The three throws are independent, so \(P(\text{no odd in 3 throws})=\left(\dfrac12\right)^3=\dfrac18\).

Step 3: Use the complement rule:
\[ P(\text{at least one odd})=1-P(\text{no odd at all})=1-\dfrac18=\dfrac78 \]

Final Answer:
\[ \boxed{\dfrac78} \]