# A die is thrown six times.the probability of getting at least a 5,five times is

2
by shubhangikhare
i think ans is 12/46656

2014-03-25T22:22:10+05:30
Total no of events=46656
Only 25 satisfy the condn
Therefore probability = 25/46656
2014-03-26T21:42:25+05:30
Solution :
Let us imagine the sample space
s=  { (1,1,1,1,1,1) ; (1,1,1,1,1,2);(1,1,1,1,1,3);(1,1,1,1,1,4);(1,1,1,1,1,5);(1,1,1,1,1,6)
(1,2,1,1,1,1);
......
......
...... (6,6,6,6,6,,6) }

Thus the number of elements in sample space would be = 6*6*6*6*6*6
=46656

Now Lets construct the possible happenings
p={ (1,5,5,5,5,5);(5,1,5,5,5,5);(5,5,1,5,5,5);(5,5,5,1,5,5);(5,5,5,5,1,5);(5,5,5,5,5,1)
(2,5,5,5,5,5);(5,2,5,5,5,5);(5,5,2,5,5,5);(5,5,5,2,5,5);(5,5,5,5,2,5);(5,5,5,5,5,2)
(3,5,5,5,5,5);(5,3,5,5,5,5);(5,5,3,5,5,5);(5,5,5,3,5,5);(5,5,5,5,3,5);(5,5,5,5,5,3)
(4,5,5,5,5,5);(5,4,5,5,5,5);(5,5,4,5,5,5);(5,5,5,4,5,5);(5,5,5,5,4,5);(5,5,5,5,5,4)
(5,5,5,5,5,5)
(6,5,5,5,5,5);(5,6,5,5,5,5);(5,5,6,5,5,5);(5,5,5,6,5,5);(5,5,5,5,6,5);(5,5,5,5,5,6)
}

Probability of getting at least five 5 is  = n(p) / n(s)
=31 / 46656