three dice are thrown simultaneously probability of getting a number on the third die greater than the sum appeared in first two die
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Three dice are thrown simultaneously.
There are 216 element in the total sample space.
Let us define an element A by assuming the numbers on the dice is 6
A=(2,2,2),(2,1,3),(2,3,1),(1,3,2),(1,2,3),(1,1,4),(4,1,1),(1,4,1),(3,1,2),(3,2,1)
B= getting a number 3 in all 3 dice =(2,2,2)
Since it is given that the event A has already occured.
i.e., the sum of the numbers on each die is 6
We have 10 cases out of which only one (2,2,2) is favourable to us.
∴P(B)=
10
1
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