- Forums
###### Proability question

watch this thread

2 weeks ago

In order to write an exam, a student needs an alarm clock to wake up, which has proven to successfully wake him 80% of the time. If he hears the alarm in the morning the probability of writing the test is 0.9 and if he doesn´t hear the alarm the probability is 0.5.

Please view link to see my working out:

https://ibb.co/NSCLMWc

Please view link to see my working out:

https://ibb.co/NSCLMWc

(edited 2 weeks ago)

Original post by As.1997

In order to write an exam, a student needs an alarm clock to wake up, which has proven to successfully wake him 80% of the time. If he hears the alarm in the morning the probability of writing the test is 0.9 and if he doesn´t hear the alarm the probability is 0.5.

Please view link to see my working out:

https://ibb.co/XYvdNyj

Please view link to see my working out:

https://ibb.co/XYvdNyj

From the defintion of conditional probability, the joint gives bayes formula as you rearrange

p(A&B) = p(A|B)p(B) = p(B|A)p(A)

so the numerator is the joint probability which you cant simply replace with the marginal p(A).

As a 2*2 table, you could imagine that you view the problem as wrote exam (rows) and heard alarm (columns). Assuming you had 100 people the joint data would be

..................... Heard | Not Heard

Wrote........... 72.......|.....10

Not Wrote..... 8.......|......10

so each cell represent the counts assoicated with joint probability p(A & B). If we know they wrote the exam, were interested in row 1 (condition on it or slice the data) and the probaiblity they heard the alarm is 72/82, so 72/(72+10).

If we just used the marginal p(heard) on the numerator that would be 80/82, wed be including the 8 who heard but did not write the exam in the calculation (80=72+8) which doesnt really make sense. If we rewrote (modify the data sllightly) the second row as 18 0 (so leave the first row unchanged), wed end up with 90/80 which is a probability > 1 so problematic.

Rather than just remembering a formula, I generally find imagining the joint as a 2d table (in this case) makes the conditioning/given idea much more intuitive as you simply slice it on a row or column, depending on what youre given and ignore the other outcomes. Its similar to a venn diagram when you focus on one of the outcomes (circles) if youre given that that outcome occurs.

(edited 2 weeks ago)

Original post by mqb2766

From the defintion of conditional probability, the joint gives bayes formula as you rearrange

p(A&B) = p(A|B)p(B) = p(B|A)p(A)

so the numerator is the joint probability which you cant simply replace with the marginal p(A).

As a 2*2 table, you could imagine that you view the problem as wrote exam (rows) and heard alarm (columns). Assuming you had 100 people the joint data would be

..................... Heard | Not Heard

Wrote........... 72.......|.....10

Not Wrote..... 8.......|......10

so each cell represent the counts assoicated with joint probability p(A & B). If we know they wrote the exam, were interested in row 1 (condition on it or slice the data) and the probaiblity they heard the alarm is 72/82, so 72/(72+10).

If we just used the marginal p(heard) on the numerator that would be 80/82, wed be including the 8 who heard but did not write the exam in the calculation (80=72+8) which doesnt really make sense. If we rewrote (modify the data sllightly) the second row as 18 0 (so leave the first row unchanged), wed end up with 90/80 which is a probability > 1 so problematic.

Rather than just remembering a formula, I generally find imagining the joint as a 2d table (in this case) makes the conditioning/given idea much more intuitive as you simply slice it on a row or column, depending on what youre given and ignore the other outcomes. Its similar to a venn diagram when you focus on one of the outcomes (circles) if youre given that that outcome occurs.

p(A&B) = p(A|B)p(B) = p(B|A)p(A)

so the numerator is the joint probability which you cant simply replace with the marginal p(A).

As a 2*2 table, you could imagine that you view the problem as wrote exam (rows) and heard alarm (columns). Assuming you had 100 people the joint data would be

..................... Heard | Not Heard

Wrote........... 72.......|.....10

Not Wrote..... 8.......|......10

so each cell represent the counts assoicated with joint probability p(A & B). If we know they wrote the exam, were interested in row 1 (condition on it or slice the data) and the probaiblity they heard the alarm is 72/82, so 72/(72+10).

If we just used the marginal p(heard) on the numerator that would be 80/82, wed be including the 8 who heard but did not write the exam in the calculation (80=72+8) which doesnt really make sense. If we rewrote (modify the data sllightly) the second row as 18 0 (so leave the first row unchanged), wed end up with 90/80 which is a probability > 1 so problematic.

Rather than just remembering a formula, I generally find imagining the joint as a 2d table (in this case) makes the conditioning/given idea much more intuitive as you simply slice it on a row or column, depending on what youre given and ignore the other outcomes. Its similar to a venn diagram when you focus on one of the outcomes (circles) if youre given that that outcome occurs.

Thank you so much! I really liked the table method!

Original post by As.1997

Thank you so much! I really liked the table method!

Its really just the joint probability which is something thats possibly a bit underemphasised at "a level".

- Probability- biased coin tossed twice
- How to revise for biology and chemistry a levels?
- I don't know how to revise for chemistry
- A Level Maths Checklist
- Senior Physics Challenge Isaac Physics
- Edexcel English Language Paper 2 advice
- psych help PLS
- Home Office AO Role
- UCAS Clearing 2023 FAQ and Help Megathread
- Got a Ucas or results related question? Ask a Clearing and Applications Advisor here
- Is it me or are there very few past paper questions on Kinetics for AS?
- Maths interview prep help
- Senior Physics Challenge 2022
- LNAT
- French speaking exam EDEXCEL
- Maths struggles
- Help! Maths A level advice
- Senior Physics Challenge 2021
- Home Office 'Strength-based interview questions.'
- Eduqas A-level English Literature Component 1 (A720U10-1) - 24th May 2023 [Exam Chat]

- GCSE Mathematics Study Group 2023-2024
- Hypothesis Testing
- Step support programme assignment 7 help pls
- Senior Maths Challenge 2023
- A-level Mathematics Study Group 2023-2024
- Dimensional Analysis
- Do we have to memorise all physics equations for GCSE 2024 ?
- Girls Maths Olympiad 2023
- Electrical Engineering maths help with Desmos graphing calculator
- A Level Maths Moments question
- Discrete maths questions
- Plotting data on a graph.
- Hypothesis Testing
- Problem solving the smc 2023
- Maths trig
- Help With A level Trig
- which calculator; the fx-991cw or fx-991ex
- AS Maths edexcel 2023
- Edexcel AS Stats and mechanics paper 2023?
- Edexcel A Level Mathematics Paper 2 unofficial mark scheme correct me if wrong

- Official: University of East Anglia (UEA) A100 2024 Entry
- Personal statement: Biological sciences
- ATAS certificate for UK for January 2024 intake
- Pharmacy URGENT!!!!!!!!!!!!!!!
- glasgow offer
- Should I call work and say I'm Sick?
- Diageo graduate scheme
- Can I evict myself from halls
- Should I return for S6 or go to college?
- accounting notes

- Cambridge Parents Association
- Girls Vs. Boys (Part 45)
- Monarchists vs Republicans
- Make your prediction: Will it SNOW this christmas?
- I'm planning to steal Christmas....AMA!
- Psychology, mental health / coaching job advice
- EY 2024 Graduate Program
- Dwp work coach september 2023 merseyside
- The Official Cambridge Applicants for 2024 Entry Thread
- The daily Wordle puzzle thread!

- Official Year 11 Chat 2023-24
- Could I quit my work to do this
- missed catchup work
- University of Oxford 2024 Undergraduate Applicants Official Thread
- Official: Kent and Medway Medical School A100 2024 entry
- is it selfish of me
- Official Imperial College London Offer Holders Thread for 2024 entry
- Can I go to uni through Ucas points if i do 1 btec and 2 alevels
- what is major pros of to get verification information more then more
- Who did you play in the school nativity?

- Christmas Countdown
- MU123 to prep for M05 Astrophysics
- Motivating myself - my GYG blog :)
- Sevenoaks waitlist
- I’m scared that my boyfriend will break up with me…
- struggle with early a level maths
- Medicine Interview Discussion 2024 Entry
- Sevenoaks School sixth form entrance
- New Thread Experience Feedback - Official Thread
- Radio Transmitters

The Student Room and The Uni Guide are both part of The Student Room Group.

© Copyright The Student Room 2023 all rights reserved

The Student Room and The Uni Guide are trading names of The Student Room Group Ltd.

Register Number: 04666380 (England and Wales), VAT No. 806 8067 22 Registered Office: Imperial House, 2nd Floor, 40-42 Queens Road, Brighton, East Sussex, BN1 3XB