Aspire Faculty ID #10354 · Topic: NIMCET 2013 · Just now
NIMCET 2013

Two fair dice are tossed. What is the probability that the total score is a prime number?

Solution

Two fair dice are tossed. We need the probability that the total score is a prime number. 
Possible sums when two dice are rolled: 
 $2,3,4,5,6,7,8,9,10,11,12$ 
Prime numbers among these are: 
 $2,3,5,7,11$ 
 Now count outcomes for each prime sum: 
 Sum = 2 → $(1,1)$ → 1 way 
 Sum = 3 → $(1,2),(2,1)$ → 2 ways 
 Sum = 5 → $(1,4),(2,3),(3,2),(4,1)$ → 4 ways 
 Sum = 7 → $(1,6),(2,5),(3,4),(4,3),(5,2),(6,1)$ → 6 ways 
 Sum = 11 → $(5,6),(6,5)$ → 2 ways 

 Total favourable outcomes: $1 + 2 + 4 + 6 + 2 = 15$ 
 Total outcomes when 2 dice are rolled: $36$ 
 Therefore, $P(\text{prime sum}) = \frac{15}{36} = \frac{5}{12}$ 
 Final Answer: $\frac{5}{12}$
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