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# A person has five tickets of a lucky draw for which a total of 12

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Manager
Joined: 18 Jul 2019
Posts: 53
A person has five tickets of a lucky draw for which a total of 12  [#permalink]

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25 Nov 2019, 01:50
2
00:00

Difficulty:

65% (hard)

Question Stats:

52% (02:19) correct 48% (01:50) wrong based on 29 sessions

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A person has five tickets of a lucky draw for which a total of 12 tickets were sold and exactly six prizes are to be given. The probability that the person will win at least one prize is

(A) $$\frac{61}{32}$$

(B)$$\frac{131}{132}$$

(C)$$\frac{31}{132}$$

(D)$$\frac{11}{12}$$

(E)$$\frac{13}{17}$$
Retired Moderator
Joined: 27 Oct 2017
Posts: 1806
WE: General Management (Education)
Re: A person has five tickets of a lucky draw for which a total of 12  [#permalink]

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29 Nov 2019, 23:39
2
Out of 12 tickets, 6 tickets are lucky tickets and other 6 are unlucky tickets
If the person gets all 5 tickets from this 6- unlucky tickets, he will not earn prize.
The no of ways of selecting 5 tickets out of 6-unlucky tickets = 6C5.

devavrat wrote:
gmatbusters
How is 6C5 / 12C5 the probability of winning no ticket?
Can you please explain in detail

_________________
Retired Moderator
Joined: 27 Oct 2017
Posts: 1806
WE: General Management (Education)
Re: A person has five tickets of a lucky draw for which a total of 12  [#permalink]

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29 Nov 2019, 09:45
P(At least one prize) = 1- P(No Prize)
= 1- (6C5)/(12C5)
= 1- (6.5.4.3.2.1)/(12.11.10.9.8)
=1-1/132
= 131/132

CaptainLevi wrote:
A person has five tickets of a lucky draw for which a total of 12 tickets were sold and exactly six prizes are to be given. The probability that the person will win at least one prize is

(A) $$\frac{61}{32}$$

(B)$$\frac{131}{132}$$

(C)$$\frac{31}{132}$$

(D)$$\frac{11}{12}$$

(E)$$\frac{13}{17}$$

_________________
Manager
Joined: 19 Feb 2019
Posts: 120
Location: India
Concentration: Marketing, Statistics
GMAT 1: 650 Q46 V34
GPA: 3
Re: A person has five tickets of a lucky draw for which a total of 12  [#permalink]

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29 Nov 2019, 23:36
gmatbusters
How is 6C5 / 12C5 the probability of winning no ticket?
Can you please explain in detail
Re: A person has five tickets of a lucky draw for which a total of 12   [#permalink] 29 Nov 2019, 23:36