1
JEE Main 2024 (Online) 27th January Morning Shift
Numerical
+4
-1
Change Language
A fair die is tossed repeatedly until a six is obtained. Let $X$ denote the number of tosses required and let

$a=P(X=3), b=P(X \geqslant 3)$ and $c=P(X \geqslant 6 \mid X>3)$. Then $\frac{b+c}{a}$ is equal to __________.
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2
JEE Main 2023 (Online) 12th April Morning Shift
Numerical
+4
-1
Change Language

A fair $$n(n > 1)$$ faces die is rolled repeatedly until a number less than $$n$$ appears. If the mean of the number of tosses required is $$\frac{n}{9}$$, then $$n$$ is equal to ____________.

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3
JEE Main 2023 (Online) 11th April Evening Shift
Numerical
+4
-1
Change Language

Let the probability of getting head for a biased coin be $$\frac{1}{4}$$. It is tossed repeatedly until a head appears. Let $$\mathrm{N}$$ be the number of tosses required. If the probability that the equation $$64 \mathrm{x}^{2}+5 \mathrm{Nx}+1=0$$ has no real root is $$\frac{\mathrm{p}}{\mathrm{q}}$$, where $$\mathrm{p}$$ and $$\mathrm{q}$$ are coprime, then $$q-p$$ is equal to ________.

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4
JEE Main 2023 (Online) 31st January Evening Shift
Numerical
+4
-1
Change Language
Let A be the event that the absolute difference between two randomly choosen real numbers in the sample space $[0,60]$ is less than or equal to a . If $\mathrm{P}(\mathrm{A})=\frac{11}{36}$, then $\mathrm{a}$ is equal to _______.
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