Question
One hundred tickets are sold in a raffle which offed
two prizes. Hazel buys five of the tickets.
A ticket is drawn at random for the first prize. A second
ticket is drawn from the remaining tickets for the other
price.
What is the probability that Hazel wins both prizes?
two prizes. Hazel buys five of the tickets.
A ticket is drawn at random for the first prize. A second
ticket is drawn from the remaining tickets for the other
price.
What is the probability that Hazel wins both prizes?
Ask by Rodriquez Reid. in Australia
Mar 30,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The probability that Hazel wins both prizes is
Solution
-
Hazel has
tickets out of total tickets. -
The probability that Hazel wins the first prize is
-
Once the first prize is awarded to one of Hazel’s tickets (assuming she wins the first prize), she has
remaining tickets out of the remaining tickets. Thus, the probability that she wins the second prize is -
The overall probability that Hazel wins both prizes is the product of the two probabilities:
Therefore, the probability that Hazel wins both prizes is
Answered by UpStudy AI and reviewed by a Professional Tutor
Like
error msg
Explain 
Simplify this solution Beyond the Answer
To find the probability that Hazel wins both prizes, we need to calculate the chance of her ticket being drawn first and then winning again with her remaining ticket. For the first prize, the probability of Hazel winning is the number of her tickets (5) divided by the total tickets (100), which is
If Hazel wins the first prize, there are now 99 tickets left, of which 4 are hers. Therefore, the probability of her winning the second prize becomes
So, the probability that Hazel wins both prizes is approximately 0.2%.
