Question

3.  A number is selected randomly from a container containing all the integers from 10 to 50. Find:

1. P(even | greater than 40)
2. P(greater than 40 | even)
3. P(prime | between 20 and 40)

Answer 1

1.

Numbers greater than 40:$41,42,43,44,45,46,47,48,49,50$

$$P(even|greater\ than\ 40)=\dfrac{5}{10}=\dfrac{1}{2}$$

2. There are 25 even numbers.

Numbers greater than 40:$41,42,43,44,45,46,47,48,49,50$

$$P(even|greater\ than\ 40)=\dfrac{5}{10}=\dfrac{1}{2}$$

Even numbers greater than 40: $42,44,46,48,50$

$$P(greater\ than\ 40|even)=\dfrac{5}{25}=\dfrac{1}{5}$$

3. There are 19 numbers between 20 and 40.

Prime numbers between 20 and 40: $23,29,31,37.$

$$P(prime|between\ 20\ and\ 40)=\dfrac{4}{19}$$