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A die is thrown three times and the sum of the three numbers is found to be 15. The probability that the first throw was a four is
A. 1/10
B. 1/6
C. 1/5
D. 1/4
E. 1/3

let, x,y,z are the three outcomes of three respective dices .
so, x+y+z= 15
case I : 5+5+5 =15 ( 1 way)
case I : 5+6+4 =15 ( 3! ways = 6 ways)
case I : 6+6+3 =15 ( 3!/2! ways = 3 ways)
so, total number of cases= 10

now, favourable case : 4 in first drawn, so 11 comes from rest two.
also,5+6 = 11 or, 6+5 =11
so, in 2 ways we can get 4 in first drawn and 15 in total.

so, required probability = 2/10 = 1/5

correct answer C
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Hi All,
What if take each throw as a mutually inclusive case?
What if 1st throw is not same as 2nd throw ?
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