conditional probability
a pair if dice is thrown. If it is known that one dice shows a 4, what probability that
a) the other dice shows a 5
Here are all 36 dice rolls
(1,1) (1,2) (1,3) (1,4) (1,5) (1,6)
(2,1) (2,2) (2,3) (2,4) (2,5) (2,6)
(3,1) (3,2) (3,3) (3,4) (3,5) (3,6)
(4,1) (4,2) (4,3) (4,4) (4,5) (4,6)
(5,1) (5,2) (5,3) (5,4) (5,5) (5,6)
(6,1) (6,2) (6,3) (6,4) (6,5) (6,6)
But since we are given that one of them is a 4, we
can eliminate all the ones that don't have one of
them a 4. That just leaves this reduced sample space
of 11 rolls.
(1,4)
(2,4)
(3,4)
(4,1) (4,2) (4,3) (4,4) (4,5) (4,6)
(5,4)
(6,4)
And therefore the probability that the other one is a 5
is the probability of rolling one of the 2 that I have
colored red below, out of the 11:
(1,4)
(2,4)
(3,4)
(4,1) (4,2) (4,3) (4,4) (4,5) (4,6)
(5,4)
(6,4)
So the answer is 2 out of 11 or 2/11.
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b)the total of both the dice is greater than 7
Since we are still given that one of them is a 4, we have the same
reduced sample space, and I'll color the ones red which have a
sum greater than 7
(1,4)
(2,4)
(3,4)
(4,1) (4,2) (4,3) (4,4) (4,5) (4,6)
(5,4)
(6,4)
That's 5 out of 11, or a probability of 5/11
Edwin
