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 _____________.

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 ___________.

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 ______________.

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 _____________.