Probability Practice, Events With and Without Replacement

There are 3 even numbers (2, 4, 6) on a 6-sided die. The probability is $$\frac{3}{6} = \frac{1}{2}$$ .

There are 5 outcomes that are not 6 (1, 2, 3, 4, 5). The probability is $$\frac{5}{6}$$ .

The probability is $$\frac{6}{15} \times \frac{5}{14} = \frac{1}{7}$$ .

'With replacement' means that after an item is drawn, it is put back into the set before the next draw, keeping the total number of items constant.

'Without replacement' means that after an item is drawn, it is not put back into the set, reducing the total number of items for the next draw.

The events are independent. The probability is $$\frac{4}{10} \times \frac{3}{10} = \frac{12}{100} = \frac{3}{25}$$ .

The probability of getting tails on a fair coin is $$\frac{1}{2}$$ .

The probability of rolling a specific number (like 3) is $$\frac{1}{6}$$ .

The combined probability is the product of their individual probabilities.

The probability is $$\frac{2}{7} \times \frac{5}{7} = \frac{10}{49}$$ .