Tina has two fair normal 6-sided dice. One is red and th other is blue. She throws both of them once. Find as a fraction in it's lowest terms, th probability that i) The red die shows a 2 and th blue die does not show a 2 ii) The sum of the two show is equal to 5 iii) One die shows a 3 and the other shows an even number.
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Let B be the event that exactly one dice shows 3
P(A) = 3/36 { (1,3), (2,2), (3,1)}
P(B) = 10/36 {(3,1) to (3,6), (1,3) to (1,6)} (not including (3,3))
P(AB) = 2/36 {(1,3), (3,1)}
Using, P(A|B) = P(AB) / P(B)
P(A|B) = 2/10
P(A) = 3/36 { (1,3), (2,2), (3,1)}
P(B) = 10/36 {(3,1) to (3,6), (1,3) to (1,6)} (not including (3,3))
P(AB) = 2/36 {(1,3), (3,1)}
Using, P(A|B) = P(AB) / P(B)
P(A|B) = 2/10
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