1
JEE Main 2021 (Online) 27th August Evening Shift
Numerical
+4
-1
The probability distribution of random variable X is given by :

X 1 2 3 4 5
P(X) K 2K 2K 3K K

Let p = P(1 < X < 4 | X < 3). If 5p = $$\lambda$$K, then $$\lambda$$ equal to ___________.
2
JEE Main 2021 (Online) 25th July Evening Shift
Numerical
+4
-1
A fair coin is tossed n-times such that the probability of getting at least one head is at least 0.9. Then the minimum value of n is ______________.
3
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 _____________.
4
JEE Main 2021 (Online) 24th February Morning Shift
Numerical
+4
-1
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 ________.