Question

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

Answer 1

Total no of events=46656
Only 25 satisfy the condn
Therefore probability = 25/46656

Answer 2

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