NDA 2023
Exam NDA
Year 2023
Subject Mathematics
Chapter Probability NDA 2023 · Mathematics · Probability
Three dice are thrown. What is the probability of getting a sum...
Three dice are thrown. What is the probability of getting a sum which is a perfect square?
Options A 17 108 \frac{17}{108} 108 17 B 5 108 \frac{5}{108} 108 5 C 19 108 \frac{19}{108} 108 19 D 23 108 \frac{23}{108} 108 23 Correct answer A. 17 108 \frac{17}{108} 108 17
Step-by-step solution
n ( s ) = 6 × 6 × 6 = 216 Since, sum is 4 = ( 1 , 1 , 2 ) → 3 ways sum is 9 = ( 1 , 2 , 6 ) → 6 ways = ( 2 , 2 , 5 ) → 3 ways = ( 3 , 1 , 5 ) → 6 ways = ( 1 , 4 , 4 ) → 3 ways = ( 3 , 2 , 4 ) → 6 ways = ( 3 , 3 , 3 ) → 1 way \begin{aligned}
\mathrm{n}(\mathrm{ s})=6 \times 6 \times 6 & =216 \\
\text{ Since, sum is } 4 & =(1,1,2) \rightarrow 3 \text{ ways } \\
\text{ sum is } 9 & =(1,2,6) \rightarrow 6 \text{ ways } \\
& =(2,2,5) \rightarrow 3 \text{ ways } \\
& =(3,1,5) \rightarrow 6 \text{ ways } \\
& =(1,4,4) \rightarrow 3 \text{ ways } \\
& =(3,2,4) \rightarrow 6 \text{ ways } \\
& =(3,3,3) \rightarrow 1 \text{ way }
\end{aligned} n ( s ) = 6 × 6 × 6 Since, sum is 4 sum is 9 = 216 = ( 1 , 1 , 2 ) → 3 ways = ( 1 , 2 , 6 ) → 6 ways = ( 2 , 2 , 5 ) → 3 ways = ( 3 , 1 , 5 ) → 6 ways = ( 1 , 4 , 4 ) → 3 ways = ( 3 , 2 , 4 ) → 6 ways = ( 3 , 3 , 3 ) → 1 way
Sum is
16 = ( 4 , 6 , 6 ) → 3 16=(4,6,6) \rightarrow 3 16 = ( 4 , 6 , 6 ) → 3 ways
= ( 5 , 5 , 6 ) → 3 ways S o , r e q u i r e d p r o b a b i l i t y = 34 216 = 17 108 =(5,5,6) \rightarrow 3 \text{ ways }
So, required probability =\frac{34}{216}=\frac{17}{108} = ( 5 , 5 , 6 ) → 3 ways S o , re q u i re d p ro babi l i t y = 216 34 = 108 17
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