A multiple choice examination has 5 questions. Each question has three alternative answers of which exactly one is correct. The probability, that a student will get 4 or more correct answers just by guessing, is
Let a random variable X have a Binomial distribution with mean 8 and variance 4 . If $\mathrm{P}(x \leqslant 2)=\frac{\mathrm{k}}{2^{16}}$, then k is equal to
For the probability distribution
| $\mathrm{X:}$ | $-2$ | $-1$ | $0$ | $1$ | $2$ | $3$ |
|---|---|---|---|---|---|---|
| $\mathrm{p}(x):$ | 0.1 | 0.2 | 0.2 | 0.3 | 0.15 | 0.05 |
Then the $\operatorname{Var}(\mathrm{X})$ is
(Given : $$\left.(0.25)^2=0.0625,(0.35)^2=0.1225,(0.45)^2=0.2025\right)$$
Two cards are drawn successively with replacement from a well- shuffled pack of 52 cards. Let X denote the random variable of number of kings obtained in the two drawn cards. Then $\mathrm{P}(x=1)+\mathrm{P}(x=2)$ equals
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