Question

What is the probability that at least one of them is selected?

Hint:

To find the probability of "at least one" event happening, use the complement rule: \( P(\textAt least one) = 1 - P(\textNone) \).

Answer 1

Step 1: Probability of no one being selected
The probability that none of them are selected is: \[ P(\text{No one selected}) = \left( 1 - \frac{1}{5} \right) \cdot \left( 1 - \frac{1}{3} \right) \cdot \left( 1 - \frac{1}{4} \right) = \frac{4}{5} \cdot \frac{2}{3} \cdot \frac{3}{4} = \frac{2}{5}. \]
Step 2: Probability of at least one being selected
The probability that at least one of them is selected is: \[ P(\text{At least one selected}) = 1 - P(\text{No one selected}) = 1 - \frac{2}{5} = \frac{3}{5}. \]
Final Result: The probability that at least one of them is selected is \( \frac{3}{5} \).