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Part a.
P(boy wins first prize) = P(first ticket is winning ticket) OR P(second ticket is winning ticket) OR P(third ticket is winning ticket)
= 1/30 + 1/30 + 1/30
= 1/10

Part b.
P(winning both) = P(winning first) AND P(winning second)

P(winning first) = P(first ticket is winning ticket) OR P(second ticket is winning ticket) OR P(third ticket is winning ticket)
= 1/10

Of the remaining 2 tickets that the boy has, one of them is the second prize ticket.
P(winning second) = P(first remaining ticket is winning ticket) OR P(second remaining ticket is winning ticket)
= 1/29 + 1/29
= 2/29

So, P(winning both) = 1/10 x 2/29
= 1/145

Part c.
P(only second prize) = P(not winning first) AND P(winning second)

We have P(winning first) from part a.
So, P(not winning first) = 1 â€“ P(winning first)
= 1 â€“ 1/10
= 9/10

P(winning second) = P(first ticket is second place ticket) OR P(second ticket is second place ticket) OR P(third ticket is second place ticket)
= 1/29 + 1/29 + 1/29
= 3/29

So, P(only second prize) = 9/10 x 3/29
= 27/290

Part d.
P(winning a prize) = 1 â€“ P(not winning any prize)

P(not winning any prize) = P(not winning 1st prize) AND P(not winning second prize)
= (1 â€“ P(winning first)) AND (1 â€“ P(winning second))
= 1 â€“ 1/10 AND 1 â€“ 3/29
= 9/10 x 26/29
= 117/145

An a small raffle, there are only 2 prizes, and 30 tickets are sold. A boy has 3 tickets in the raffle. Find the probability that he wins

(a) first prize, (b) both prize, (c) only the 2nd prize, and (d) a prize.

a) 3/30
b)3/30*2/29
c)27/30*3/29
d)1-[27/30*26/29]

explanation same as duttsit but the figures are different for me.
i haven't reduced the fractions as it would be easier to associate the figures with the question.