A bag contains black and white counters, and the probability of selecting a black counter is $\frac{1}{6}$.

Without replacement, three counters are taken from the bag and they are all black. What is the smallest possible number of white counters in the bag?

Find the probability that the number rolled with an ordinary fair die is:

a prime number or a $4$

Find the probability that the number rolled with an ordinary fair die is:

a square number or a multiple of $3$

Find the probability that the number rolled with an ordinary fair die is:

more than $3$ or a factor of $8$ .

A group of $40$ students took a test in Economics. The following Venn diagram shows that $19$ boys $\left(\mathrm{B}\right)$ took the test and that seven students failed the test $\left(F\right)$

Describe the $21$ students who are members of the set $B^{\text{'}}$.

A group of $40$ students took a test in Economics. The following Venn diagram shows that $19$ boys $\left(\mathrm{B}\right)$ took the test and that seven students failed the test $\left(F\right)$

Find the probability that a randomly selected student is a boy or someone who failed the test.