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# A polling company reports that there is a 40% chance that a

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Manager
Joined: 07 Dec 2010
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Concentration: Marketing, General Management
A polling company reports that there is a 40% chance that a  [#permalink]

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Updated on: 05 Aug 2019, 19:25
1
6
00:00

Difficulty:

15% (low)

Question Stats:

77% (01:35) correct 23% (01:50) wrong based on 176 sessions

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A polling company reports that there is a 40% chance that a certain candidate will win the next election. If the candidate wins, there is a 60% chance that she will sign Bill X and no other bills. If she decides not to sign Bill X, she will sign either Bill Y or Bill Z, chosen randomly. What is the chance that the candidate will sign Bill Z?

A. 10 %
B. 8 %
C. 6 %
D. 4 %
E. 5 %

Originally posted by ruturaj on 11 Aug 2011, 22:18.
Last edited by generis on 05 Aug 2019, 19:25, edited 3 times in total.
Renamed the topic and edited the question.
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Re: A polling company reports that there is a 40% chance that a  [#permalink]

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11 Aug 2011, 22:23
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Fairly straight forward...

40% - Candidate Elected
100%-60% = 40% - Candidate does not sigh Bill X
50% - Candidate randomly chooses between two bills.

These are multiplicative:

40% x 40% x 50%
0.4 x 0.4 x 0.5 = 0.08 = 8%

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Re: A polling company reports that there is a 40% chance that a  [#permalink]

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11 Aug 2011, 23:38
assume 0.5 for y or z just like heads or tails for a coin.

hence, 0.4 * 0.4 * 0.5 = 0.08 or 8%

B it is.
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Re: A polling company reports that there is a 40% chance that a  [#permalink]

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23 Dec 2011, 03:16
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To solve this kind of questions, it's better to use probability tree. It's a good way to reach the right answer and avoid making mistake.
Attachment:

prob.jpg [ 18.62 KiB | Viewed 4091 times ]
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Re: A polling company reports that there is a 40% chance that a  [#permalink]

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23 Dec 2011, 23:51
2/5*(2/5)/2=.08=8%
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Re: A polling company reports that there is a 40% chance that a  [#permalink]

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22 Oct 2016, 10:50
ruturaj wrote:
A polling company reports that there is a 40% chance that a certain candidate will win the next election. If the candidate wins, there is a 60% chance that she will sign Bill X and no other bills. If she decides not to sign Bill X, she will sign either Bill Y or Bill Z, chosen randomly. What is the chance that the candidate will sign Bill Z?

A. 10
B. 8
C. 6
D. 4
E. 5

Chance of winning the election is 2/5

Chance of winning the election and signing Bill X is 2/5*3/5 => 6/25

Chance of winning the election and not signing Bill X is 2/5*2/5 => 4/25

Chance of winning the election and not signing Bill X and selecting either Bill Y or Bill Z is 1/2*2/5*2/5 => 2/25 = 2/25*100 = 8

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Re: A polling company reports that there is a 40% chance that a  [#permalink]

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02 Jan 2017, 05:59
40% if win * 40% if choose other than X * 50% if choose Z = 8%. Too easy :D
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Re: A polling company reports that there is a 40% chance that a  [#permalink]

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08 Jul 2017, 23:47
Choosing a smart number 100 can also help?? Is that a correct way ??
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Re: A polling company reports that there is a 40% chance that a  [#permalink]

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04 Jul 2018, 19:32
ruturaj wrote:
A polling company reports that there is a 40% chance that a certain candidate will win the next election. If the candidate wins, there is a 60% chance that she will sign Bill X and no other bills. If she decides not to sign Bill X, she will sign either Bill Y or Bill Z, chosen randomly. What is the chance that the candidate will sign Bill Z?

A. 10
B. 8
C. 6
D. 4
E. 5

The candidate will win with 40% = 2/5 probability.

After she wins, she will sign Bill X with 60% = 3/5 probability; therefore, she has a 40% = 2/5 chance of signing other bills. Since she will sign either Bill Y or Bill Z with an equal chance, she has a 50% = 1/2 probability of signing Bill Z. Therefore, if she is elected, the probability she will sign Bill Z is

2/5 x 2/5 x 1/2 = 2/25 = 8/100 = 8%.

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Re: A polling company reports that there is a 40% chance that a  [#permalink]

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10 Sep 2018, 08:04
ruturaj wrote:
A polling company reports that there is a 40% chance that a certain candidate will win the next election. If the candidate wins, there is a 60% chance that she will sign Bill X and no other bills. If she decides not to sign Bill X, she will sign either Bill Y or Bill Z, chosen randomly. What is the chance that the candidate will sign Bill Z?

A. 10
B. 8
C. 6
D. 4
E. 5

Dear Moderator,

The answer choices should be in percentage. Hope you will do the needful. Thank you.
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Re: A polling company reports that there is a 40% chance that a   [#permalink] 10 Sep 2018, 08:04
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