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The length of Alice's commute, in minutes, differs depending on whethe

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Mbawarrior01
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The length of Alice's commute, in minutes, differs depending on whethe [#permalink] New post   20 Nov 2016, 09:44
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A. \(\frac{2}{7}\)

B. \(\frac{3}{8}\)

C. \(\frac{3}{7}\)

D. \(\frac{1}{2}\)

E. \(\frac{5}{7}\)


Show Spoiler

The length of Alice's commute, in minutes, differs depending on whether it's a weekday or weekend.

The probability of how long the weekday commute will take is included in the table below.

0 - 15 Minutes 15 - 30 Minutes 30 - 45 Minutes 45 Minutes or More
0.05 0.25 0.4 0.3


The probability of how long the weekend commute will take is included in the table below.

0 - 15 Minutes 15 - 30 Minutes 30 - 45 Minutes 45 Minutes or More
0.25 0.50 0.15 0.1


If Alice's commute took 30 minutes or less today, what is the probability that today is a weekday? Assume Alice commutes every day and that weekdays are considered to be Monday-Friday.
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I have no clue how to go about this question
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louwi
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Re: The length of Alice's commute, in minutes, differs depending on whethe [#permalink] New post   21 Nov 2016, 16:06
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I'm not sure my thinking is correct but I got the right answer.
so my guess was:
Probability of being on a week day= 5/7
Probability of having a commute of 30 minutes or less on a week day: 0.40+0.25+0.05=0.7

Probability of having a commute of 30 minutes or less and being on a weekday is : (5/7)*(0.7)= 1/2

AC:D
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KarishmaB
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The length of Alice's commute, in minutes, differs depending on whethe [#permalink] New post   Updated on: 17 Oct 2022, 02:14
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Mbawarrior01 wrote:
The length of Alice's commute, in minutes, differs depending on whether it's a weekday or weekend.

The probability of how long the weekday commute will take is included in the table below.

0 - 15 Minutes 15 - 30 Minutes 30 - 45 Minutes 45 Minutes or More
0.05 0.25 0.4 0.3


The probability of how long the weekend commute will take is included in the table below.

0 - 15 Minutes 15 - 30 Minutes 30 - 45 Minutes 45 Minutes or More
0.25 0.50 0.15 0.1


If Alice's commute took 30 minutes or less today, what is the probability that today is a weekday? Assume Alice commutes every day and that weekdays are considered to be Monday-Friday.


\(\frac{2}{7}\)

\(\frac{3}{8}\)

\(\frac{3}{7}\)

\(\frac{1}{2}\)

\(\frac{5}{7}\)

Show Spoiler
I have no clue how to go about this question


P(B given A) = P(A and B)/P(A)
P('Weekday' given '30 mins or less') = P(Weekday and 30 mins or less) / P(30 mins or less)

P(Weekday and 30 mins or less) = (5/7) * 0.3 = 1.5/7
P(30 mins or less) = (5/7) * 0.3 + (2/7) * .75 = 3/7

P('Weekday' given '30 mins or less') = (1.5/7) / (3/7) = 1/2

Originally posted by KarishmaB on 21 Nov 2016, 23:10.
Last edited by KarishmaB on 17 Oct 2022, 02:14, edited 1 time in total.
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Naveen1821
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Re: The length of Alice's commute, in minutes, differs depending on whethe [#permalink] New post   02 Jan 2017, 04:37
Probability required = Probability that today is weekday and not weekend
= {P(0-15 weekday) x ((1 - P(0-15 weekend))} + {P(15-30 weekday) x ((1 - P(15-30 weekend))}
= {0.05 x (1- 0.25)} + {0.25 x (1- 0.5)}
= 0.5
Choise D = 1/2
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Re: The length of Alice's commute, in minutes, differs depending on whethe [#permalink] New post   30 Apr 2020, 07:31
louwi wrote:
I'm not sure my thinking is correct but I got the right answer.
so my guess was:
Probability of being on a week day= 5/7
Probability of having a commute of 30 minutes or less on a week day: 0.40+0.25+0.05=0.7

Probability of having a commute of 30 minutes or less and being on a weekday is : (5/7)*(0.7)= 1/2

AC:D


Hi,
In your solution, how come you're including 0.4 as a probability weekday/30 minutes or less? The 0.4 probability falls under the 30-45 minute 'bucket'

Thank you,
Chris
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Re: The length of Alice's commute, in minutes, differs depending on whethe [#permalink] New post   20 Feb 2024, 22:12
KarishmaB wrote:
Mbawarrior01 wrote:
The length of Alice's commute, in minutes, differs depending on whether it's a weekday or weekend.

The probability of how long the weekday commute will take is included in the table below.

0 - 15 Minutes 15 - 30 Minutes 30 - 45 Minutes 45 Minutes or More
0.05 0.25 0.4 0.3


The probability of how long the weekend commute will take is included in the table below.

0 - 15 Minutes 15 - 30 Minutes 30 - 45 Minutes 45 Minutes or More
0.25 0.50 0.15 0.1


If Alice's commute took 30 minutes or less today, what is the probability that today is a weekday? Assume Alice commutes every day and that weekdays are considered to be Monday-Friday.


\(\frac{2}{7}\)

\(\frac{3}{8}\)

\(\frac{3}{7}\)

\(\frac{1}{2}\)

\(\frac{5}{7}\)

Show Spoiler
I have no clue how to go about this question


P(B given A) = P(A and B)/P(A)
P('Weekday' given '30 mins or less') = P(Weekday and 30 mins or less) / P(30 mins or less)

P(Weekday and 30 mins or less) = (5/7) * 0.3 = 1.5/7
P(30 mins or less) = (5/7) * 0.3 + (2/7) * .75 = 3/7

P('Weekday' given '30 mins or less') = (1.5/7) / (3/7) = 1/2

­Hi KarishmaB, I did not get this solution. Can you please help me understand this. Thank you in advance.
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KarishmaB
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The length of Alice's commute, in minutes, differs depending on whethe [#permalink] New post   21 Feb 2024, 21:42
Expert Reply
samarpan.g28 wrote:
KarishmaB wrote:
Mbawarrior01 wrote:
The length of Alice's commute, in minutes, differs depending on whether it's a weekday or weekend.

The probability of how long the weekday commute will take is included in the table below.

0 - 15 Minutes 15 - 30 Minutes 30 - 45 Minutes 45 Minutes or More
0.05 0.25 0.4 0.3


The probability of how long the weekend commute will take is included in the table below.

0 - 15 Minutes 15 - 30 Minutes 30 - 45 Minutes 45 Minutes or More
0.25 0.50 0.15 0.1


If Alice's commute took 30 minutes or less today, what is the probability that today is a weekday? Assume Alice commutes every day and that weekdays are considered to be Monday-Friday.


\(\frac{2}{7}\)

\(\frac{3}{8}\)

\(\frac{3}{7}\)

\(\frac{1}{2}\)

\(\frac{5}{7}\)

Show Spoiler
I have no clue how to go about this question


P(B given A) = P(A and B)/P(A)
P('Weekday' given '30 mins or less') = P(Weekday and 30 mins or less) / P(30 mins or less)

P(Weekday and 30 mins or less) = (5/7) * 0.3 = 1.5/7
P(30 mins or less) = (5/7) * 0.3 + (2/7) * .75 = 3/7

P('Weekday' given '30 mins or less') = (1.5/7) / (3/7) = 1/2

­Hi KarishmaB, I did not get this solution. Can you please help me understand this. Thank you in advance.



 

It's conditional probability. It is calculated as P(B given A) = P(A and B)/P(A)
I do not have a blog post or a YouTube video on it at this time but I do discuss it in detail in my content at anaprep.com. For now, all the content is freely available to everyone every Sunday (under the Super Sundays program) so you can check it out this Sunday. 
­­
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Re: The length of Alice's commute, in minutes, differs depending on whethe [#permalink] New post   21 Feb 2024, 22:36
KarishmaB wrote:
Quote:
 

It's conditional probability. It is calculated as P(B given A) = P(A and B)/P(A)
I do not have a blog post or a YouTube video on it at this time but I do discuss it in detail in my content at anaprep.com. For now, all the content is freely available to everyone every Sunday (under the Super Sundays program) so you can check it out this Sunday. 
­­­

Thank you KarishmaB, I am following your content. It is helpful :)
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Re: The length of Alice's commute, in minutes, differs depending on whethe [#permalink]
21 Feb 2024, 22:36
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