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Probability

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Q JEE MAIN 2026
A bag contains 10 balls out of which $k$ are red and $(10-k)$ are black, where $0 \leq k \leq 10$. If three balls are...
JEE Main Mathematics Hard
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Q JEE MAIN 2026
From a lot containing 10 defective and 90 non-defective bulbs, 8 bulbs are selected one by one with replacement. Then the probability of getting at...
JEE Main Mathematics Easy
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Q JEE MAIN_2026_
From the first 100 natural numbers, two numbers first $a$ and then $b$ are selected randomly without replacement. If the probability that $a-b \geqslant 10$...
JEE Main Mathematics Medium
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Q JEE MAIN 2026
Let $n$ be the number obtained on rolling a fair die. If the probability that the system $$ \begin{aligned} & x-\mathrm{n} y+z=6 \\ & x+(\mathrm{n}-2)...
JEE Main Mathematics Medium
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Q JEE MAIN_2026
If a random variable X has the probability distribution then $\mathrm{P}(3
JEE Main Mathematics Medium
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Q JEE MAIN_2026_
Two distinct numbers $a$ and $b$ are selected at random from $1,2,3, \ldots, 50$. The probability, that their product ab is divisible by 3 ,...
JEE Main Mathematics Medium
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Q JEE MAIN 2026
A random variable X takes values $0,1,2,3$ with probabilities $\frac{2 a+1}{30}, \frac{8 a-1}{30}, \frac{4 a+1}{30}, b$ respectively, where $\mathrm{a}, \mathrm{b} \in \mathrm{R}$. Let $\mu$ and...
JEE Main Mathematics Medium
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Q JEE MAIN_2019_
Assume that each born child is equally likely to be a boy or a girl. If two families have two children each, then the conditional...
JEE Main Mathematics Easy
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Q JEE MAIN 2019
Four persons can hit a target correctly with probabilities $\frac{1}{2}, \frac{1}{3}, \frac{1}{4}$ and $\frac{1}{8}$ respectively. If all hit at the target independently, then the probability...
JEE Main Mathematics Medium
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Q JEE Advanced 2025
A factory has a total of three manufacturing units, $M_1, M_2$, and $M_3$, which produce bulbs independent of each other. The units $M_1, M_2$, and...
JEE Advance Mathematics Easy
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