One hundred tickets are sold in a raffle which offers two prizes - HSC - SSCE Mathematics Standard - Question 23 - 2023 - Paper 1

If Hazel wins the first prize, the remaining tickets are 99, and Hazel still has 4 tickets left. Therefore, the probability that Hazel wins the second prize is:

$P(Hazel ext{ wins second prize}) = \frac{4}{99}$

The overall probability that Hazel wins both prizes is the product of the probabilities of winning each prize:

$P(wins ext{ both prizes}) = P(Hazel ext{ wins first prize}) \times P(Hazel ext{ wins second prize})$

Substituting the values:

$P(wins both prizes) = \frac{5}{100} \times \frac{4}{99} = \frac{20}{9900} = \frac{1}{495}$