JEE Mains · Maths · STD 12 - 13. probability
A coin is tossed \(8\) times. If the probability that exactly \(4\) heads appear in the first six tosses and exactly \(3\) heads appear in the last five tosses is \(p\), then \(96p\) is equal to _____.
- A 5
- B 8
- C 7
- D 9
Answer & Solution
Correct Answer
(D) 9
Step-by-step Solution
Detailed explanation
Let the outcomes of the \(8\) tosses be denoted by \(X_1, X_2, X_3, X_4, X_5, X_6, X_7, X_8\). Let \(A\) be the number of heads in the first \(3\) tosses (\(X_1, X_2, X_3\)). Let \(B\) be the number of heads in the next \(3\) tosses (\(X_4, X_5, X_6\)). Let \(C\) be the number…
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 \(\vec{a}=\hat{i}+\hat{j}+2 \hat{k}, \vec{b}=2 \hat{i}-3 \hat{j}+\hat{k}\) and \(\overrightarrow{ c }=\hat{ i }-\hat{ j }+\hat{ k }\) be three given vectors. Let \(\vec{v}\) be a vector in the plane of \(\vec{a}\) and \(\overrightarrow{ b }\) whose projection on \(\overrightarrow{ c }\) is \(\frac{2}{\sqrt{3}}\). If \(\overrightarrow{ v } . \hat{ j }=7\), then \(\overrightarrow{ v } \cdot(\hat{ i }+\hat{ k })\) is equal toJEE Mains 2022 Medium
- Let \((\alpha, \beta, \gamma)\) be the foot of perpendicular from the point \((1,2,3)\) on the line \(\frac{x+3}{5}=\frac{y-1}{2}=\frac{z+4}{3}\). then \(19(\alpha+\beta+\gamma)\) is equal to :JEE Mains 2024 Hard
- Let \(f(x)=4 \cos ^3 x+3 \sqrt{3} \cos ^2 x-10\). The number of points of local maxima of \(f\) in interval \((0,2 \pi)\) is:JEE Mains 2024 Hard
- Let \((a, b)\) be the point of intersection of the curve \(x^2=2 y\) and the straight line \(y-2 x-6=0\) in the second quadrant. Then the integral \(I=\int_a^b \frac{9 x^2}{1+5^x} d x\) is equal to :JEE Mains 2025 Medium
- For the system of linear equations \(a x+y+z=1\), \(x+a y+z=1, x+y+a z=\beta\), which one of the following statements is NOT correct ?JEE Mains 2023 Hard
- Let \(a\) and \(\mathrm{b}\) respectively be the points of local maximum and local minimum of the function \(f(x)=2 x^{3}-3 x^{2}-12 x .\) If \(A\) is the total area of the region bounded by \(\mathrm{y}=\mathrm{f}(\mathrm{x})\), the \(\mathrm{x}\)-axis and the lines \(x=a\) and \(x=b\), then \(4 A\) is equal to ..... .JEE Mains 2021 Hard
More PYQs from JEE Mains
- Let the mean and the variance of \(5\) observations \(x_{1}, x_{2}, x_{3}, x_{4}, x_{5}\) be \(\frac{24}{5}\) and \(\frac{194}{25}\) respectively. If the mean and variance of the first \(4\) observation are \(\frac{7}{2}\) and \(a\) respectively, then \(\left(4 a+x_{5}\right)\) is equal toJEE Mains 2022 Hard
- If \(\frac{1}{\sqrt{1}+\sqrt{2}}+\frac{1}{\sqrt{2}+\sqrt{3}}+\ldots+\frac{1}{\sqrt{99}+\sqrt{100}}=m\) and \(\frac{1}{1 \cdot 2}+\frac{1}{2 \cdot 3}+\ldots+\frac{1}{99 \cdot 100}=\mathrm{n}\), then the point \((\mathrm{m}, \mathrm{n})\) lies on the lineJEE Mains 2024 Hard
- For the system of linear equations \(x+y+z=6\) ; \(\alpha x+\beta y+7 z=3\) ; \(x+2 y+3 z=14\) which of the following is \(NOT\) true ?JEE Mains 2023 Hard
- Let \(S=2+\frac{6}{7}+\frac{12}{7^{2}}+\frac{20}{7^{3}}+\frac{30}{7^{4}}+\ldots . .\) then \(4 S\) is equal toJEE Mains 2022 Hard
- Let \((2,3)\) be the largest open interval in which the function \(f(x)=2 \log _{\mathrm{e}}(x-2)-x^2+a x+1\) is strictly increasing and (b, c) be the largest open interval, in which the function \(\mathrm{g}(x)=(x-1)^3(x+2-\mathrm{a})^2\) is strictly decreasing. Then \(100(a+b-c)\) is equal to :JEE Mains 2025 Medium
- Let the points \(\left(\frac{11}{2}, \alpha\right)\) lie on or inside the triangle with sides \(x+y=11, x+2 y=16\) and \(2 x+3 y=29\). Then the product of the smallest and the largest values of \(\alpha\) is equal to :JEE Mains 2025 Medium