List of top Statistics Questions on Probability and Uniform Distribution

If a fair coin is tossed 5 times, what is the probability of getting exactly 3 heads?

If $f(x) = \begin{cases} 3(1 - 2x^2), & 0<x<1 \\ 0, & \text{otherwise} \end{cases}$ is a probability density function of $X$, then $P\left(\frac{1}{4}<x<\frac{1}{3}\right)$ is