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

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BTGmoderatorLU: Moderator; Posts: 2505; Joined: Sun Oct 15, 2017 1:50 pm; Followed by:6 members

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

by BTGmoderatorLU » Sat Jun 30, 2018 4:48 pm

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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

The OA is B.

Please, can someone assist me with this PS questions? I don't have clear what can I do to solve it. Thanks in advance!

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Source: Beat The GMAT — Problem Solving | Sat Jun 30, 2018 4:48 pm

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by [email protected] » Sun Jul 01, 2018 10:24 am

Hi All,

We're told that 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 does not to sign Bill X, she will sign either Bill Y or Bill Z, chosen randomly. The 'intent' of this question is to ask for the percentage chance that the candidate will sign Bill Z.

To start, this is an oddly-worded question, but it's essentially a big Probability question (with each additional 'step' decreasing the probability of the end result). For Bill Z to get signed, a number of events have to occur first:
-This one candidate must win the election. (40% chance)
-The candidate must NOT sign Bill X. (40% chance)
-Between Bill Y and Bill Z, Bill Z must be the one that's randomly chosen (50% chance)

The probability of all of these events occurring is (.4)(.4)(.5) = .080 = 8%

Final Answer: B

GMAT assassins aren't born, they're made,
Rich

Contact Rich at [email protected]

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8086; Joined: Sat Apr 25, 2015 10:56 am; Location: Los Angeles, CA; Thanked: 43 times; Followed by:29 members

by Scott@TargetTestPrep » Wed Jul 04, 2018 6:31 pm

BTGmoderatorLU 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%.

Answer: B

Scott Woodbury-Stewart
Founder and CEO
[email protected]

See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews

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Shahrukh_mbabreakspace: Senior | Next Rank: 100 Posts; Posts: 32; Joined: Mon Jul 02, 2018 1:56 am; Followed by:2 members

by Shahrukh_mbabreakspace » Wed Jul 04, 2018 11:03 pm

Chance of winning election = 40%
Chance of selecting y or z if she won= (100-60)=40%
Since she selects randomly between y and z, chance of selecting z if she wins = 40/2= 20%

So, overall chance of selecting z= 40%*20%= 8%

________________________________________

Shahrukh Moin Khan
QA Mentor at Breakspace
https://www.mbabreakspace.com
PGDM: IIM Calcutta
B.Tech IIT Roorkee