# stats : bayes theoremWatch

This discussion is closed.
#1
Your wallet contains a single note which you think is equally likely to
be either £10 or £20. You add a £10 note without looking. Later, you
remove one of the two notes at random, again without looking inside
the wallet. It's a £10 note. What is the chance the other note is £20?
try first then see what i did wrong (in white)

i said

let A be event £10, B be event £20
P(A) = P(B) = 1/2

(B^c is complement of B)

then P(B|A) = P(A|B)P(B) / [P(A|B)P(B) + P(A|B^c)P(B^c)] by Bayes Theorem

= 0.5*0.5 / (0.5*0.5 + 0.5*0.5)
=1/2

but the answer is 1/3 ?!
0
14 years ago
#2
(Original post by kikzen)
Your wallet contains a single note which you think is equally likely to
be either £10 or £20. You add a £10 note without looking. Later, you
remove one of the two notes at random, again without looking inside
the wallet. It's a £10 note. What is the chance the other note is £20?
try first then see what i did wrong (in white)

i said

let A be event £10, B be event £20
P(A) = P(B) = 1/2

(B^c is complement of B)

then P(B|A) = P(A|B)P(B) / [P(A|B)P(B) + P(A|B^c)P(B^c)] by Bayes Theorem

= 0.5*0.5 / (0.5*0.5 + 0.5*0.5)
=1/2

but the answer is 1/3 ?!

P(B^c) = 1, not (1/2)

P(B|A) = P(A|B)P(B) / [P(A|B)P(B) + P(A|B^c)P(B^c)]

=> 0.5*0.5 / (0.5*0.5 + 0.5*1)
=> (1/4)/(1/4 + 1/2)
=> (1/4)/(3/4)
=> 1/3

Euclid.
0
14 years ago
#3
p(x=20)=0.5
p(x=10)=0.5
then you add a £10 note
=> p(x=30)=0.5 p(x=20)=0.5
you take out a note, y
p(y=10)=0.5 (it being the 2nd note) + 0.5x0.5 (it being the first note, which is a £10 note)= *0.75* =>p(y=20)=*0.25*
Turn out its a £10 note. (ie probability=0.75)
So *given that* its a £10, whats the chance the other is a £20:
0.25/0.75 = 1/3
0
#4
is P(B^c) = 1 because you already have £10 in your hand? if not ,why not?!
0
14 years ago
#5
(Original post by kikzen)
is P(B^c) = 1 because you already have £10 in your hand? if not ,why not?!
Yes, P(B^c) is the chance of already having chosen £10, which is 1.

Euclid.
0
#6
euclid youll get some rep soon; gotta spread it around first apparently
0
14 years ago
#7
(Original post by kikzen)
euclid youll get some rep soon; gotta spread it around first apparently
thank you.
0
14 years ago
#8
thank you kikzen for my rep!
0
#9
ya welcome
0
X
new posts
Latest
My Feed

### Oops, nobody has postedin the last few hours.

Why not re-start the conversation?

see more

### See more of what you like onThe Student Room

You can personalise what you see on TSR. Tell us a little about yourself to get started.

### University open days

• University of East Anglia
All Departments Open 13:00-17:00. Find out more about our diverse range of subject areas and career progression in the Arts & Humanities, Social Sciences, Medicine & Health Sciences, and the Sciences. Postgraduate
Wed, 30 Jan '19
• Aston University
Wed, 30 Jan '19
• Solent University
Sat, 2 Feb '19

### Poll

Join the discussion

Remain (1388)
79.59%
Leave (356)
20.41%