Question

Two dice are thrown together. If the numbers appearing on the two dice are different, then what is the probability that the sum is $6$ $?$

• A. $\frac{5}{36}$
• B. $\frac{1}{6}$
• C. $\frac{2}{15}$
• D. None of these

Answer 1

The correct option is C

$\frac{2}{15}$

Find the required probability:

When two dice are thrown, total number of sample space is $=6^2=36$

Total number of cases, that the numbers appearing on the dice are same $=6$

Hence, the total number of cases, the numbers appearing on the dice are different $=36-6=30$

Total number of cases when the sum of numbers is $6=\left\{(1,5),(5,1),(2,4),(4,2)\right\}=4$

Hence, the required probability $=\frac{\mathrm{number}\mathrm{of}\mathrm{favorable}\mathrm{outcomes}}{\mathrm{total}\mathrm{number}\mathrm{of}\mathrm{outcomes}}=\frac{4}{30}=\frac{2}{15}$

Hence, option (C) is correct.