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# An a small raffle, there are only 2 prizes, and 30 tickets

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Intern
Joined: 18 Aug 2005
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An a small raffle, there are only 2 prizes, and 30 tickets [#permalink]  06 Nov 2005, 17:05
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.
VP
Joined: 22 Aug 2005
Posts: 1120
Location: CA
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(a) p (winning first prize) = total tickets he has/total number of tickets
= 3/20

(b) p(winning both prizes)
= p (winning first) * p(winning second)
= 3/20 * 2/19

(c) p(winning only second prize)
= p(first miss) * p(second win)
= 17/20 * 3/19

(d) p(winning a prize)
= 1- p(not winning any prize)
= 1 - 3/20 * 3/19
Intern
Joined: 18 Aug 2005
Posts: 17
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Kudos [?]: 0 [0], given: 0

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

So, P(winning a prize) = 1 â€“ 117/145
= 28/145
Manager
Joined: 11 Jul 2005
Posts: 86
Location: New York
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Re: Probability [#permalink]  06 Nov 2005, 18:50
sandman wrote:
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.
Senior Manager
Joined: 19 Feb 2005
Posts: 486
Location: Milan Italy
Followers: 1

Kudos [?]: 11 [0], given: 0

duttsit wrote:
(a) p (winning first prize) = total tickets he has/total number of tickets
= 3/20

(b) p(winning both prizes)
= p (winning first) * p(winning second)
= 3/20 * 2/19

(c) p(winning only second prize)
= p(first miss) * p(second win)
= 17/20 * 3/19

(d) p(winning a prize)
= 1- p(not winning any prize)
= 1 - 3/20 * 3/19

alright the tickets are 30
and then for last question it is 1- 27/30*26/29
Senior Manager
Joined: 14 Apr 2005
Posts: 418
Location: India, Chennai
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Re: Probability [#permalink]  06 Nov 2005, 22:59
(a) first prize,
3/30

(b) both prize,
(3/30)*(2/29)

(c) only the 2nd prize, and
(27/30)*(3/29)

(d) a prize.
1-P(No prize)
1- ((3/30)(2/29))
Director
Joined: 27 Jun 2005
Posts: 513
Location: MS
Followers: 2

Kudos [?]: 36 [0], given: 0

1) First Prize = 3/30=>1/10

2) both Prize = 3/30*2/29=>2/290

3) Only Second = 9/10*3/29

4) a Prize = 1-(9/10*26/29)

SVP
Joined: 28 May 2005
Posts: 1740
Location: Dhaka
Followers: 6

Kudos [?]: 75 [0], given: 0

1) 3/30=1/10

2) 3/30*2/29=2/290

3) 9/10*3/29 = 27/290

4) 1-(9/10*26/29)
_________________

hey ya......

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