Question 1

A dice is rolled three times and sum of three numbers appearing on the uppermost face is 15. The chance that the first roll was a four is

Solution

There are three possibilities for sum of uppermost faces of dice is equal to 15. They are

5, 5, 5 - only 1 arrangement

4, 5, 6 - 3! = 6 arrangements

3, 6, 6 - $$\frac{3!}{2}$$ = 3 arrangements

Out of these 10 arrangements, there are 2 cases in which 4 occurs in first roll ( 4,5,6 or 4,6,5)

Therefore, probability = $$\frac{2}{10}$$ = $$\frac{1}{5}$$

Answer is option B.

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