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1
JEE Main 2021 (Online) 17th March Morning Shift
Numerical
+4
-1
Let there be three independent events E1, E2 and E3. The probability that only E1 occurs is $$\alpha$$, only E2 occurs is $$\beta$$ and only E3 occurs is $$\gamma$$. Let 'p' denote the probability of none of events occurs that satisfies the equations
($$\alpha$$ $$-$$ 2$$\beta$$)p = $$\alpha$$$$\beta$$ and ($$\beta$$ $$-$$ 3$$\gamma$$)p = 2$$\beta$$$$\gamma$$. All the given probabilities are assumed to lie in the interval (0, 1).

Then, $$\frac{Probability\ of\ occurrence\ of\ E_{1}}{Probability\ of\ occurrence\ of\ E_{3}}$$ is equal to _____________.
2
JEE Main 2021 (Online) 24th February Morning Slot
Numerical
+4
-1
English
Hindi
Let Bi (i = 1, 2, 3) be three independent events in a sample space. The probability that only B1 occur is $$\alpha$$, only B2 occurs is $$\beta$$ and only B3 occurs is $$\gamma$$. Let p be the probability that none of the events Bi occurs and these 4 probabilities satisfy the equations $$\left( {\alpha - 2\beta } \right)p = \alpha \beta$$ and $$\left( {\beta - 3\gamma } \right)p = 2\beta \gamma$$ (All the probabilities are assumed to lie in the interval (0, 1)).
Then $${{P\left( {{B_1}} \right)} \over {P\left( {{B_3}} \right)}}$$ is equal to ________.
3
JEE Main 2020 (Online) 5th September Evening Slot
Numerical
+4
-0
In a bombing attack, there is 50% chance that a bomb will hit the target. Atleast two independent hits are required to destroy the target completely. Then the minimum number of bombs, that must be dropped to ensure that there is at least 99% chance of completely destroying the target, is ______.
The probability of a man hitting a target is $${1 \over {10}}$$. The least number of shots required, so that the probability of his hitting the target at least once is greater than $${1 \over {4}}$$, is _____.