Question:
If two dice are thrown, find the probability that the sum is neither 5 nor 9?
यदि दो पासे फेंके जाते हैं, तो योग के न तो 5 और न ही 9 होने की प्रायिकता ज्ञात कीजिए।
Options:
- \(\frac{3}{9}\)
- \(\frac{5}{9}\)
- \(\frac{1}{9}\)
- \(\frac{7}{9}\)
- \(\frac{3}{9}\)
- \(\frac{5}{9}\)
- \(\frac{1}{9}\)
- \(\frac{7}{9}\)
Correct Answer: d)
Explanation:
Total number of outcomes when two dice are thrown = \(6 \times 6 = 36\).
– Outcomes where sum is 5: \((1,4), (2,3), (3,2), (4,1)\) (4 outcomes)
– Outcomes where sum is 9: \((3,6), (4,5), (5,4), (6,3)\) (4 outcomes)
Total outcomes with sum 5 or 9 = \(4 + 4 = 8\).
\[ P(\text{sum is 5 or 9}) = \frac{8}{36} = \frac{2}{9} \]
\[ P(\text{sum is neither 5 nor 9}) = 1 – \frac{2}{9} = \frac{7}{9} \]
दो पासों को फेंकने पर कुल संभावित परिणाम = \(6 \times 6 = 36\)।
– योग 5 वाले परिणाम: \((1,4), (2,3), (3,2), (4,1)\) (4 परिणाम)
– योग 9 वाले परिणाम: \((3,6), (4,5), (5,4), (6,3)\) (4 परिणाम)
योग 5 या 9 होने के कुल परिणाम = \(4 + 4 = 8\)।
\[ P(\text{योग 5 या 9}) = \frac{8}{36} = \frac{2}{9} \]
\[ P(\text{योग न तो 5 और न ही 9}) = 1 – \frac{2}{9} = \frac{7}{9} \]