JEE Mains · Maths · STD 11 - 14. probability
Let Ajay will not appear in JEE exam with probability \(\mathrm{p}=\frac{2}{7}\), while both Ajay and Vijay will appear in the exam with probability \(\mathrm{q}=\frac{1}{5}\). Then the probability, that Ajay will appear in the exam and Vijay will not appear is :
- A \(\frac{9}{35}\)
- B \(\frac{18}{35}\)
- C \(\frac{24}{35}\)
- D \(\frac{3}{35}\)
Answer & Solution
Correct Answer
(B) \(\frac{18}{35}\)
Step-by-step Solution
Detailed explanation
\( \mathrm{P}(\overline{\mathrm{A}})=\frac{2}{7}=\mathrm{p} \) \( \mathrm{P}(\mathrm{A} \cap \mathrm{V})=\frac{1}{5}=\mathrm{q} \) \( \mathrm{P}(\mathrm{A})=\frac{5}{7} \) \( \text { Ans. } \mathrm{P}(\mathrm{A} \cap \overline{\mathrm{V}})=\frac{18}{35}\)
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
- Let two vertices of triangle \(ABC\) be \((2,4,6)\) and \((0,-2,-5)\), and its centroid be \((2,1,-1)\). If the image of third vertex in the plane \(x+2 y+4 z=11\) is \((\alpha, \beta, \gamma)\), then \(\alpha \beta+\beta \gamma+\gamma \alpha\) is equal toJEE Mains 2023 Hard
- Let \(a , b , c\) and \(d\) be positive real numbers such that \(a+b+c+d=11\). If the maximum value of \(a^5 b^3 c^2 d\) is \(3750 \beta\), then the value of \(\beta\) isJEE Mains 2023 Hard
- Bag A contains 9 white and 8 black balls, while bag B contains 6 white and 4 black balls. One ball is randomly picked up from the bag B and mixed up with the balls in the bag A. Then a ball is randomly drawn from the bag A. If the probability that the ball drawn is white is \( p/q \) (where \( gcd(p,q)=1 \)), then \( p+q \) is equal to:JEE Mains 2026 Easy
- The area of the region enclosed by the curve \(f(x)=\max \{\sin x, \cos x\},-\pi \leq x \leq \pi\) and the \(x\)-axis isJEE Mains 2023 Medium
- Let \(A\) and \(B\) be two \(3 \times 3\) real matrices such that \(\left(A^{2}-B^{2}\right)\) is invertible matrix. If \(A^{5}=B^{5}\) and \(A^{3} B^{2}=A^{2} B^{3}\), then the value of the determinant of the matrix \(A^{3}+B^{3}\) is equal to:JEE Mains 2021 Hard
- If \(\frac{{{}^{n + 2}{C_6}}}{{{}^{n - 2}{P_2}}} = 11\), then \(n\) satisfies the equationJEE Mains 2016 Hard
More PYQs from JEE Mains
- Let PQ be a focal chord of the parabola \(y^2=36 x\) of length \(100\), making an acute angle with the positive \(x\)-axis. Let the ordinate of \(P\) be positive and \(M\) be the point on the line segment \(P Q\) such that \(P M: M Q=3: 1\). Then which of the following points does NOT lie on the line passing through \(M\) and perpendicular to the line \(PQ\) ?JEE Mains 2023 Hard
- Let the foot of perpendicular from a point \(P(1,2,-1)\) to the straight line \(L: \frac{x}{1}=\frac{y}{0}=\frac{z}{-1}\) be \(N\). Let a line be drawn from \(P\) parallel to the plane \(x+y+2 z=0\) which meets \(L\) at point \(Q\). If \(\alpha\) is the acute angle between the lines \(\mathrm{PN}\) and \(\mathrm{PQ}\), then \(\cos \alpha\) is equal to \(.....\)JEE Mains 2021 Hard
- The \(8^{\text {th }}\) common term of the series \(S _1=3+7+11+15+19+\ldots . .\) ; \(S _2=1+6+11+16+21+\ldots .\) is \(.......\).JEE Mains 2023 Medium
- The number of times the digit \(3\) will be written when listing the integers from \(1\) to \(1000\) isJEE Mains 2021 Medium
- Let \(\mathrm{A}=\{x \in(0, \pi) -\left\{\frac{\pi}{2}\right\}: \log _{(2 / \pi)}|\sin x|+\log _{(2 / \pi)}|\cos x|=2\}\) and \(\mathrm{B}=\{x \geqslant 0: \sqrt{x}(\sqrt{x}-4)-3|\sqrt{x}-2|+6=0\}\). Then \(\mathrm{n}(\mathrm{A} \cup \mathrm{B})\) is equal to :JEE Mains 2025 Medium
- Let \(a_{1}=b_{1}=1, a_{n}=a_{n-1}+2\) and \(b_{n}=a_{n}+b_{n-1}\) for every natural number \(n \geq 2\). Then \(\sum_{ n =1}^{15} a _{ n } \cdot b _{ n }\) is equal to \(.........\)JEE Mains 2022 Hard