Probability Questions

In throwing a six-faced die, let A be the event that an even number occurs, B be the event that an odd number occurs, and C be the event that a number greater than 3 occurs. Which one of the following is correct?

Let $f(x)=c{x}^2$ for $x=1,2,3$. The value of constant $c$ such that $f$ satisfies the conditions of being a probability mass function (PMF) is:

A fair die is tossed thrice. If the probabilities of zero, one, two, and three successes are $8/27,4/9,2/9,\text{ and }1/27$ respectively, find the mean of the number of successes.

Given $P(H)=0.3$, $P(R)=0.4$, and $P(H|R)=0.2$. Find $P(R\cap H)$.

In the following table, $x$ is the discrete random variable and $p(x)$ is the probability density function. The standard deviation of $x$ is:| $x$ | $1$ | $2$ | $3$ | $4$ ||---|---|---|---|---|| $p(x)$ | $0.2$ | $0.4$ | $0.3$ | $0.1$ |

What is the probability of getting a numbered card when a card is drawn from a 52-card pack?