2U Probability Question (1 Viewer)

[BrickHead]

Hello, can someone help me with this probability question (2U Fitzpatrick):
In a raffle, 30 tickets are sold and there are two prizes. What is the probability that the person buying 5 tickets wins:
(a) neither prize
(b) both prizes
(c) at least one prize

 

[Lucas_]

a) Neither prize requires both unfavorable outcomes. Ie chance of no prize x no prize again
5/30 = chance of winning, or 25/30 chance of not winning. So 5/6 x 24/29 (1 ticket already drawn so 29 possible tickets left)
= 20/29 chance of winning neither prize or 69%

b) Both prizes requires both favorable outcomes. Ie chance of prize x prize
= 5/30 x 4/29
= 2/87 chance of winning both prizes or 0.2% chance

c) At least prize only has the outcome of NP (no prize) X NP (no prize) , so either P (prize) x P (prize) , P x NP or NP x P will yield us at least "one" prize so we must sum the probability of these 3 events. OR since we know that anything BUT NP x NP will give favorable result, we can go 1 - Probabily of NP X NP
= 1 - 20/29 = 9/29 probability of at least one prize or 31% chance

nb: If any of my above answers are wrong please correct me

 

[BrickHead]

Thank you , they match up with the answers in the back of the book.

 

[Lucas_]

Anytime mate