JEE Mains · Maths · STD 12 - 13. probability
A die is thrown two times and the sum of the scores appearing on the die is observed to be a multiple of \(4\). Then the conditional probability that the score \(4\) has appeared at least once is
- A \(\frac{1}{8}\)
- B \(\frac{1}{9}\)
- C \(\frac{1}{3}\)
- D \(\frac{1}{4}\)
Answer & Solution
Correct Answer
(B) \(\frac{1}{9}\)
Step-by-step Solution
Detailed explanation
A : Sum obtained is a multiple of 4 \(A=\{(1,3),(2,2),(3,1),(2,6),(3,5),(4,4),(5,3),(6,2),(6,6)\}\) \(B\) : Score of \(4\) has appeared at least once. \(B=\{(1,4),(2,4),(3,4),(4,4),(5,4),(6,4),(4,1),\) \((4,2),(4,3),(4,5),(4,6)\}\) Required probability…
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 \(\mathrm{A}=\left[\begin{array}{ll}1 & 2 \\ 0 & 1\end{array}\right]\) and \(\mathrm{B}=\mathrm{I}+\operatorname{adj}(\mathrm{A})+(\operatorname{adj} \mathrm{A})^2+\ldots+\) \((\operatorname{adj} \mathrm{A})^{10}\). Then, the sum of all the elements of the matrix \(B\) is :JEE Mains 2024 Medium
- Let \(\alpha, \beta(\alpha \neq \beta)\) be the values of m , for which the equations \(x+y+z=1 ; x+2 y+4 z=\mathrm{m}\) and \(x+4 y+10 z=m^2\) have infinitely many solutions. Then the value of \(\sum_{n=1}^{10}\left(n^\alpha+n^\beta\right)\) is equal to :JEE Mains 2025 Easy
- If the following system of linear equations \(2 x+y+z=5\) \(x-y+z=3\) \(x+y+a z=b\) has no solution, then :JEE Mains 2021 Hard
- In a set of \(2n\) distinct observations, each of the observations below the median of all the observations is increased by \(5\) and each of the remaining observations is decreased by \(3\). Then the mean of the new set of observationsJEE Mains 2014 Hard
- Let \(y=y(x)\) be the solution of the differential equation \(\left(1+x^2\right) \frac{d y}{d x}+y=e^{\tan ^{-1} x}, y(1)=0\). Then \(\mathrm{y}(0)\) isJEE Mains 2024 Hard
- In a game two players \(A\) and \(B\) take turns in throwing a pair of fair dice starting with player \(A\) and total of scores on the two dice, in each throw is noted. \(A\) wins the game if he throws a total of \(6\) before \(B\) throws a total of \(7\) and \(B\) wins the game if he throws a total of \(7\) before \(A\) throws a total of six The game stops as soon as either of the players wins. The probability of \(A\) winning the game isJEE Mains 2020 Hard
More PYQs from JEE Mains
- The number of non-empty equivalence relations on the set \(\{1,2,3\}\) is :JEE Mains 2025 Easy
- If \(\lim _{x \rightarrow 0} \frac{\sin ^{-1} x-\tan ^{-1} x}{3 x^{3}}\) is equal to \(L,\) then the value of \((6 L +1)\) isJEE Mains 2021 Hard
- Let \(f(x)=\int \frac{d x}{x^{\left(\frac{2}{3}\right)}+2 x^{\left(\frac{1}{2}\right)}}\) be such that \(f(0)=-26+24 \log _{ e }(2)\). If \(f (1)= a + b \log _{ e }(3)\), where \(a , b \in Z\), then \(a + b\) is equal to:JEE Mains 2026 Hard
- Let \(\vec a\, = \,\hat i\, + \,\hat j\, + \,\sqrt 2 \hat k,\,\,\vec b\, = \,{b_1}\hat i\, + \,{b_2}\hat j\, + \sqrt 2 \hat k\) and \(\vec c\, = \,5\hat i\, + \,\hat j + \sqrt 2 \hat k\) be three vectors such that the projection vector of \(\vec b\) on \(\vec a\) is \(\vec a\). If \(\vec a\, + \vec b\) is perpendicular to \(\vec c\) , then \(\left| {\vec b} \right|\) is equal toJEE Mains 2019 Hard
- The total number of words (with or without meaning) that can be formed out of the letters of the word '\(DISTRIBUTION\)' taken four at a time, is equal to ...........JEE Mains 2024 Hard
- Let \(f: R \rightarrow R\) be a function defined as \(f(x)=a \sin \left(\frac{\pi[x]}{2}\right)+[2-x], a \in R\), where [t] is the greatest integer less than or equal to \(t\). If \(\lim _{x \rightarrow-1} f(x)\) exists, then the value of \(\int_{0}^{4} f(x) d x\) is equal to.JEE Mains 2022 Hard