1
JEE Main 2021 (Online) 31st August Morning Shift
Numerical
+4
-1
An electric instrument consists of two units. Each unit must function independently for the instrument to operate. The probability that the first unit functions is 0.9 and that of the second unit is 0.8. The instrument is switched on and it fails to operate. If the probability that only the first unit failed and second unit is functioning is p, then 98 p is equal to _____________.
2
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 ___________.
3
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 ______________.
4
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 _____________.
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