If the p.m.f of a. r.v. $$X$$ is given by

$$P(X=x)=\frac{{ }^5 C_x}{2^5}$$

if $$x=0,1,2, \ldots \ldots . .5=0$$,

0 , otherwise,

then which of the following is not true?

Let $X$ be the number of successes in ' $n$ ' independent Bernoulli trials with probability of success $p=\frac{3}{4}$. The least value of ' $n$ ' so that $P(X \geq 1) \geq 0.9375$ is ......

The probability that three cards drawn from a pack of 52 cards, all are red is

$$\begin{aligned} &\text { The pdf of a random variable } X \text { is }\\ &\begin{aligned} f(x) & =3\left(1-2 x^2\right), & & 0< x<1 \\ & =0 & & \text { otherwise } \end{aligned} \end{aligned}$$

The $P\left(\frac{1}{4}< x<\frac{1}{3}\right)=\ldots$