enEnglishguગુજરાતી
JEE Mains · Maths · STD 11 - 14. probability
Let \(E\) and \(F\) be two independent events. The probability that both \(E\) and \(F\) happen is \(\frac{1}{12}\) and the probability that neither \(E\) nor \(F\) happens is \(\frac{1}{2}\) , then a value of \(\frac{{P(E)}}{{P\left( F \right)}}\) is
- A \(\frac{4}{3}\)
- B \(\frac{3}{2}\)
- C \(\frac{1}{3}\)
- D \(\frac{5}{12}\)
Answer & Solution
Correct Answer
(A) \(\frac{4}{3}\)
Step-by-step Solution
Detailed explanation
\(P\left( {E \cap F} \right) = P(E) \cdot P(F) = \frac{1}{{12}}\) \(P\left( {\bar E \cap \bar F} \right) = P(\bar E) \cdot P(\bar F) = \frac{1}{2}\) \((1-P(E))(1-P(F))=\frac{1}{2}\) Let \(P(E)=x\) \(P(F) =y \) \(=1-x-y+x y=\frac{1}{2}\)…
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
- Two tangents are drawn from a point \((- 2, - 1)\) to the curve, \(y^2 = 4x.\) If \(\alpha \) is the angle between them, then \(\left| {\tan \,\alpha } \right|\) is equal toJEE Mains 2014 Hard
- Let ABC be the triangle such that the equations of lines \(A B\) and \(A C\) be \(3 y-x=2\) and \(x+y=2\), respectively, and the points B and C lie on x -axis. If \(P\) is the orthocentre of the triangle \(A B C\), then the area of the triangle PBC is equal toJEE Mains 2025 Easy
- The number of ordered pairs ( \(\mathrm{r}, \mathrm{k}\) ) for which \(6 \cdot ^{35} \mathrm{C}_{\mathrm{r}}=\left(\mathrm{k}^{2}-3\right)\cdot{^{36} \mathrm{C}_{\mathrm{r}+1}}\). where \(\mathrm{k}\) is an integer, isJEE Mains 2020 Hard
- A person forgets his \(4-\)digit \(ATM\) pin code. But he remembers that in the code all the digits are different, the greatest digit is \(7\) and the sum of the first two digits is equal to the sum of the last two digits. Then the maximum number of trials necessary to obtain the correct code is \(...........\).JEE Mains 2023 Hard
- The system of linear equations \(x + \lambda y - z = 0,\lambda x - y - z = 0\;,\;x + y - \lambda z = 0\) has a non-trivial solution for:JEE Mains 2016 Medium
- The number of points, at which the function \(f ( x )\) \(=|2 x+1|-3|x+2|+\left|x^{2}+x-2\right|, x \in R\) is not differentiable, is ............JEE Mains 2021 Medium
More PYQs from JEE Mains
- If \(a_r\) is the coefficient of \(x^{10-r}\) in the Binomial expansion of \((1+x)^{10}\), then \(\sum \limits_{r=1}^{10} r^3\left(\frac{a_r}{a_{r-1}}\right)^2\) is equal toJEE Mains 2023 Hard
- The solution of the differential equation \(\frac{d y}{d x}-\frac{y+3 x}{\log _{e}(y+3 x)}+3=0\) is (where \(C\) is a constant of integration.)JEE Mains 2020 Medium
- The maximum value of \(f(x)=\left|\begin{array}{ccc} \sin ^{2} x & 1+\cos ^{2} x & \cos 2 x \\ 1+\sin ^{2} x & \cos ^{2} x & \cos 2 x \\ \sin ^{2} x & \cos ^{2} x & \sin 2 x \end{array}\right|, x \in R \text { is }\)JEE Mains 2021 Medium
- Let \(A=\left[\begin{array}{l}1 \\ 1 \\ 1\end{array}\right]\) and \(B=\left[\begin{array}{ccc}9^{2} & -10^{2} & 11^{2} \\ 12^{2} & 13^{2} & -14^{2} \\ -15^{2} & 16^{2} & 17^{2}\end{array}\right]\), then the value of \(A ^{\prime} BA\) is.JEE Mains 2022 Medium
- Let the tangent and normal at the point \((3 \sqrt{3}, 1)\) on the ellipse \(\frac{x^2}{36}+\frac{y^2}{4}=1\) meet the \(y\)-axis at the points \(A\) and \(B\) respectively. Let the circle \(C\) be drawn taking \(A B\) as a diameter and the line \(x =2 \sqrt{5}\) intersect \(C\) at the points \(P\) and \(Q\). If the tangents at the points \(P\) and \(Q\) on the circle intersect at the point \((\alpha, \beta)\), then \(\alpha^2-\beta^2\) is equal toJEE Mains 2023 Hard
- Let \(f, g: R \rightarrow R\) be two real valued functions defined as \(f(x)=\left\{\begin{array}{cl}-|x+3| & , \quad x<0 \\ e^{x} & , \quad x \geq 0\end{array}\right.\) and \(g(x)=\left\{\begin{array}{ll}x^{2}+k_{1} x & , \quad x<0 \\ 4 x+k_{2} & , \quad x \geq 0\end{array}\right.\), where \(k_{1}\) and \(k_{2}\) are real constants. If \((gof)\) is differentiable at \(x=0\), then \((gof) (-4)+(gof)\, (4)\) is equal toJEE Mains 2022 Hard