JEE Mains · Maths · STD 12 - 13. probability
If a point \(A ( x , y )\) lies in the region bounded by the \(y\)-axis, straight lines \(2 y+x=6\) and \(5 x-6 y=30\), then the probability that \(y <1\) is
- A \(\frac{1}{6}\)
- B \(\frac{5}{6}\)
- C \(\frac{2}{3}\)
- D \(\frac{6}{7}\)
Answer & Solution
Correct Answer
(B) \(\frac{5}{6}\)
Step-by-step Solution
Detailed explanation
Required probability \(=\frac{\operatorname{ar}( ADEC )}{\operatorname{ar}( ABC )}\) \(=1-\frac{\operatorname{ar}( BDE )}{\operatorname{ar}( ABC )}\) \(=1-\frac{\frac{1}{2} \times 2 \times 4}{\frac{1}{2} \times 8 \times 6}=1-\frac{1}{6}=\frac{5}{6}\)
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