MHT CET · Maths · Probability
\(A, B, C\) are three events, one of which must and only one can happen the odds in favour of \(A\) are \(4: 6\), odds against \(B\) are \(7: 3\), then odds against \(C\) are
- A 7:3
- B 3:7
- C 6:4
- D 4:6
Answer & Solution
Correct Answer
(A) 7:3
Step-by-step Solution
Detailed explanation
\(P(A)=\frac{4}{4+6}=\frac{2}{5}, P(B)=\frac{3}{3+7}=\frac{3}{10}\)
\(\because A, B\) and \(C\) are mutually exclusive and exhaustive
\(\begin{aligned}
& \Rightarrow P(A)+P(B)+P(C)=1 \\
& \Rightarrow \frac{2}{5}+\frac{3}{10}+P(C)=1 \\
& \Rightarrow P(C)=\frac{3}{10}
\end{aligned}\)
Now, odds against to the event \(C=\frac{1-P(C)}{P(C)}=\frac{1-\frac{3}{10}}{\frac{3}{10}}=\frac{7}{3}\)
\(\because A, B\) and \(C\) are mutually exclusive and exhaustive
\(\begin{aligned}
& \Rightarrow P(A)+P(B)+P(C)=1 \\
& \Rightarrow \frac{2}{5}+\frac{3}{10}+P(C)=1 \\
& \Rightarrow P(C)=\frac{3}{10}
\end{aligned}\)
Now, odds against to the event \(C=\frac{1-P(C)}{P(C)}=\frac{1-\frac{3}{10}}{\frac{3}{10}}=\frac{7}{3}\)
See the Complete Solution
Get step-by-step explanations for this and 2.5 Lakh+ more JEE, NEET & CET questions.
- Unlock all solutions
- Practice the full chapter
- Track accuracy across PYQs
4.8 rated on Google Play · 14,000+ reviews
More questions from Maths
- The rate of disintegration of a radio active element at time \(t\) is proportional to its mass at that time. Then the time during which the original mass of \(6 \mathrm{gm}\) will disintegrate into its mass of \(3 \mathrm{gm}\) is proportional toMHT CET 2022 Hard
- In a triangle \(\mathrm{ABC}\) with usual notations, if \(\frac{\cos A}{a}=\frac{\cos B}{b}=\frac{\cos C}{c}\), then area ofMHT CET 2020 Medium
- With usual notations in \(\Delta \mathrm{ABC}, \mathrm{a}=3, \mathrm{c}=2\) and \(\sin \mathrm{C}=\frac{2}{3}\), then \(\angle \mathrm{A}=\)MHT CET 2020 Easy
- Let \(\bar{a}=\hat{i}+\hat{j}, \overline{\mathrm{~b}}=2 \hat{i}-\hat{\mathrm{k}}, \overline{\mathrm{c}}=3 \hat{i}-\hat{\mathrm{j}}+\hat{\mathrm{k}}\), then vector \(\overline{\mathrm{p}}\) satisfying \(\overline{\mathrm{p}} \cdot \bar{a}=0\) and \(\overline{\mathrm{p}} \times \overline{\mathrm{b}}=\overline{\mathrm{c}} \times \overline{\mathrm{b}}\) isMHT CET 2025 Medium
- If \((\mathrm{a}+\mathrm{b}) \cos \mathrm{C}+(\mathrm{b}+\mathrm{c}) \cos \mathrm{A}+(\mathrm{c}+\mathrm{a}) \cos \mathrm{B}=72\) and if \(\mathrm{a}=18, \mathrm{~b}=24\), then area of the triangle ABC isMHT CET 2024 Hard
- Five persons \(\mathrm{A}, \mathrm{B}, \mathrm{C}, \mathrm{D}\) and \(\mathrm{E}\) are seated in a circular arrangement. If each of them is given a cap of one of the three colours red, blue and green, then the number of ways of distributing the caps such that the persons seated in adjacent seats get different coloured caps, isMHT CET 2023 Easy
More PYQs from MHT CET
- Which of following is an aldohexose?MHT CET 2021 Easy
- Using variation of force and time given below, final velocity of a particle of mass \(2 \mathrm{~kg}\) moving with initial velocity \(6 \mathrm{~m} / \mathrm{s}\) will be
MHT CET 2023 Medium - Methanococcus converts acetate to form _________.MHT CET 2024 Hard
- The time period \(T\) of a satellite is related to the density \((\rho)\) of the plane which is orbiting close around the planet as.MHT CET 2022 Medium
- Cavity enclosed by medulla oblongata of brain is ____________ .MHT CET 2023 Easy
- Which among the following is an example of zero order reaction?MHT CET 2020 Easy