Question

A number is selected randomly from a container containing all the integers from 5 to 35. find P(odd | greater than 20)

Answer 1

By definition,

$\displaystyle P(A|B) = \frac{P(AB)}{P(B)}$

where $P(AB)$ is the probability that number is odd and greater than 20, $P(B)$ - number is greater than 20.

There are 31 integer number from 5 to 35. Among them, there are 15 numbers that are greater than 20. The amount of numbers that are odd and greater than 20 is 7. Therefore,

$\displaystyle P(AB) = \frac{7}{31}, \; P(B) = \frac{15}{31}$

and

$\displaystyle P(A|B) = \frac{P(AB)}{P(B)}=\frac{7}{15}$

Answer: 7/15