Find $P\left(x\right)$P(x) using the probability density function for the hypergeometric distribution if $N=10$N=10, $k=6$k=6, $n=3$n=3 and $x=0$x=0.
A jury of $4$4 people is formed by randomly selecting from a group of $6$6 women and $3$3 men.
Find the probability that $2$2 women are selected.
In a group of $11$11 people, $5$5 have blue eyes. If $4$4 people are randomly selected from the group, what is the probability that all of them have blue eyes?
A hoverboard manufacturer produced $140$140 hoverboards, $10%$10% of which contained faulty batteries. If a sample of $15$15 hoverboards was taken without replacement, what is the probability that less than $3$3 hoverboards contained faulty batteries?
Give your answer to four decimal places.