A sock contains 2 red marbles and an unknown number of blue marbles. Tom places a new marble in the sock. Jason puts his hand in the sock and pulls out a red marble.
What is the probability that the marble Tom put in the sock was red?
I've been trying to approach this with Bayes' Theorem but not making any progress:
P(A l B) = P(B l A) * P(A) / P(B)
I'm confused as to what A and B would represent in the problem.
Appreciate the help, thanks!
I don't understand how you set up the problem like you did. What do the terms in your numerator and denominator represent?
Here is what I get:
P(A l B) = (P(B l A) * P(A)) / P(B)
A is Tom putting a red marble in the sock.
B is Jason taking a red marble out of the sock.
P (B l A) = 3 / (x+3)
P (A) = unknown, let it be p
P (B) = p*(3/(x+3)) + (1-p)*(2/(x+2))
So
P(A l B) = (P(B l A) * P(A)) / P(B) = (3p/(x+3)) / (p*(3/(x+3)) + (1-p)*(2/(x+2)))
I end up with 3/2 p. I know I did something wrong, but I'm not sure what.
Hello, Penguins!
I agree with Mr. F
We want: . .[1]A sock contains 2 red marbles and an unknown number of blue marbles.
Tom places a new marble in the sock.
Jason puts his hand in the sock and pulls out a red marble.
What is the probability that the marble Tom put in the sock was red?
The sock contains: 2 Red and Blue marbles.
There are two cases to consider:
[1] A Red marble is added.
. . .The sock contains: 3 Red and Blue.
. . . . Then: . .[2]
[2] A Blue marble is added.
. . .The sock contains: 2 Red and Blue.
. . . . Then: .
Hence: . .[3]
Substitute [2] and [3] into [1]: .
I see what you're doing, but isn't it a problem that you're assuming the probability of Tom putting a red marble in the sock to be 1/2? I set up the problem using p as this probability and unfortunately made a careless mistake in my previous post, but get the answer to the question as (3p)/(2+p). When p = 1/2, the answer is 3/5.
I'm curious as to whether there is a rule in a situation like this as to whether lacking more information it is assumed that all possibilities have equal likelihood?
Thanks for the replies!