Question

Two uniform dice marked $1$ to $6$ are thrown together. The probability that the score on the two dice is at least seven is

• A. $\frac{5}{12}$
• B. $\frac{7}{12}$
• C. $\frac{3}{4}$
• D. $\frac{1}{2}$

Answer 1

The correct option is B $\frac{7}{12}$

Probability that the score on the two dice is at least seven$=$ $1$ $-$ Probability when score on the two dice is less than seven.

There are following cases when score on the two dice is less than seven:

When sum is $2:(1,1);3:(1,2)(2,1);4:(1,3)(2,2)(3,1);5:(1,4)(2,3)(3,2)(4,1);6:(1,5)(2,4)(3,3)(4,2)(5,1)$ $=15$ cases.

Probability that the score on the two dice is at least seven$=1-\frac{15}{6\times 6}=\frac{7}{12}$