Data:
Four fair six-sided dice are rolled
\({\rm{Probability}} = \frac{{\rm{X}}}{{1296}}\)
Formula:
\({\rm{Probability}} = \frac{{{\rm{Number\;of\;favourable\;outcomes}}}}{{{\rm{Total\;outcomes}}}}\)
Calculation:
Since 4 dice are rolled
Total outcomes = 6 × 6 × 6 × 6 = 1296
Sum of the results is 22 = Number of Favourable outcomes
Case 1: Three 6’s and one 4, for example: 6,6,6,4 (sum is 22)
Number of Favourable outcomes = 4
{(6,6,6,4), (6,6,4,6), (6,4,6,6), (4,6,6,6)}
Case 2: Two 6’s and two 5’s for example: 6,6,5,5 (sum is 22)
Number of Favourable outcomes = 6
{(6,6,5,5) (6,5,5,6) (5,5,6,6) (5,6,6,5) (6,5,6,5), (5,6,5,6) }
Total Number of Favourable outcomes = 10
Therefore, the value of X is 10.
