AP EAMCET · Maths · Probability
Three dice are thrown simultaneously and the sum of the numbers appeared on them is noted. If \(A\) is the event of getting a sum greater than 14 and \(B\) is the event of getting a sum which is a multiple of 3, then \(\mathrm{P}(\mathrm{A} \cap \overline{\mathrm{B}})+\mathrm{P}(\overline{\mathrm{A}} \cap \mathrm{B})=\)
- A \(\frac{35}{108}\)
- B \(\frac{17}{54}\)
- C \(\frac{45}{108}\)
- D \(\frac{5}{54}\)
Answer & Solution
Correct Answer
(A) \(\frac{35}{108}\)
Step-by-step Solution
Detailed explanation
\(N = 6^3 = 216\) \(n(S=15)=10, n(S=16)=6, n(S=17)=3, n(S=18)=1\) \(n(A) = n(S>14) = 10+6+3+1 = 20\) \(n(S=3)=1, n(S=6)=10, n(S=9)=25, n(S=12)=25, n(S=15)=10, n(S=18)=1\) \(n(B) = n(S \in \{3,6,9,12,15,18\}) = 1+10+25+25+10+1 = 72\)…
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