(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

In a vessel is a 5 cent coin and two 1-cent coins. If someone takes up two randomly chosen of these coins, and we let X be the total value of the coins taken, what is the probability function for X?

2. Relevant equations

I know that X has a value {2,6}

3. The attempt at a solution

I get two solutions that I do not understand which one is right:

Solution 1:

Let A1 be first coin is 1cent, A2 second coin is 1 cent

we know P(A1) = 2/3

If we want to get 2 cent : P(A1∩A2) = P(A2|A1) * P(A1)

P(A2|A1) = Conditional probability = First coin is 1 cent , second coin is 1 cent = 1/2

then P(A1∩A2) = 1/3 = P(X=2 cent)

And P(X=6 cent) = 1-P(X=2 cent) = 2/3

Solution 2 :

If I assume that the first coin A1 is 5 cent and the other is A2, 1 cent :

P(A2|A1)= 1

P(A1∩A2) = P(A2|A1) * P(A1) = 1* 1/3 = 1/3 = P(X=6) !

Solution 3:

A1 is 1 cent and A2 is 5 cent:

P(A2|A1)=1/2

P(X=6) = P(A2|A1) * P(A1) = 1/2 * 2/3 = 1/3 !

Now I get dizziness!

What is the real value of P(X=6) and P(X=2) ?!

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# A paradox in probability theory and statistics

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