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Study Stuff for MCA Examinations - NIMCET
Study Stuff for MCA Examinations - NIMCET
Previous Year Question (PYQs)
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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