SOLUTION: Four dice are thrown. What is the probability that one of the rolls is a 6, given that one of the rolls is a 2?

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Question 538727: Four dice are thrown. What is the probability that one of the rolls is a 6, given that one of the rolls is a 2?
Answer by AnlytcPhil(1810)   (Show Source): You can put this solution on YOUR website!
Four dice are thrown. What is the probability that one of the rolls is a 6, given that one of the rolls is a 2?

This is a conditional probability   P(A|B) =  = 



               number of rolls with both a 2 and a 6  
Probability = --------------------------------------------
                     number of rolls with a 6

We calculate the denominator first:

denominator =  =  - 

denominator = 6×6×6×6 - 5×5×5×5 = 64 - 54 = 1296 - 625 = 671

numerator = 

We use the formula 

     N(A or B) = N(A) + N(B) - N(A and B) 

Solving for N(A and B),

    N(A and B) = N(A) + N(B) - N(A or B)     

numerator =  =  +  - 

We have already calculated  = 671

and

 is the same quantity, that is, it is also 671

Now we only need to calculate 

 =  -  = 64 - 44 = 1296 - 256 = 1040

Now we go back to:

numerator =  =  +  -  = 671 + 671 - 1040 = 302.
 
Therefore the desired probability is .

Edwin
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