Discrete Random Variables

3 students are selected at random from the students who study Science.

Find the probability that at least 1 of these students studies Drama.

10 students are selected at random from the students who study Science.

Find the probability that more than 7 study Art or Music.

Find $P(X = 8)$.

Find $P(X < 9)$.

Find the probability that a 3 is obtained for the second time before the 6th throw.

Draw up the probability distribution table for $X$.

Find $E(X)$ and $Var(X)$.

A random sample of 80 pupils from this school is chosen.

Use an approximation to find the probability that fewer than 27 pupils have music lessons.

A random sample of 10 pupils from this school is now chosen.

Find the probability that no more than 2 pupils have music lessons.

Draw up the probability distribution table for $X$, giving the probabilities as numerical fractions.

Find $\mathrm{E}(X)$.

Find $\mathrm{P}(X \neq 2 \mid X > 0)$.

Find the probability that a 6 is obtained for the first time on the 8th throw.

Find the probability that a 6 is obtained for the third time on the 7th throw.

Find the probability, that in a week (7 days), Cooper wears a blue jumper on at least 5 days.

Use a suitable approximation to find the probability that, in any 150-day period, Cooper does not wear a jumper on fewer than 22 days.

Find the probability that the first head is obtained on the 5th throw.

Find the probability that the first head is obtained after the 6th throw.

Draw up the probability distribution table for $X$.

Find $\text{Var}(X)$.