Question

Two uniform dice marked $1$ to $6$ are thrown together. The probability that the sum is not a prime number is

• A. $\frac{1}{4}$
• B. $\frac{5}{12}$
• C. $\frac{7}{12}$
• D. $\frac{9}{12}$

Answer 1

Answer: (C)

$\frac{7}{12}$

Cases in which the sum can be a prime number are $(1,1),(1,2),(2,1),(1,4),(2,3),(3,2),(4,1),(1,6),(2,5),(3,4),(4,3),(5,2),(6,1),(5,6),(6,5)$
Number of cases with sum as prime number $=15$
Number of cases when sum is not a prime number $=36-15=21$
Total number of cases $=36$
Probability $=\frac{21}{36}=\frac{7}{12}$