Question

In one type of state lottery 5 distinct numbers are picked from 1,2,3,...,40 uniformly at random.

Answer 1

Answer: a) 1 / ⁴⁰C₅ b)  0.33

Step-by-step explanation:

a) The sample space consists of all numbers 1-40.

Since any of the number can be taken from the sample space  so each of five 5 distinct numbers we take has equal probability of occurring. So probability of each 5 numbers set we take will be equal to 1 / ⁴⁰C₅

b)

If we pick exactly 3 even number then that means other 2 will be odd.

So, we have sample space of 40 numbers out of which 20 are even and 20 are odd.

Now we have to pick 3 even out of 20 and 2 odd out of 20.

Probability = ²⁰C₃ * ²⁰C₂ / ⁴⁰C₅

Probability= 0.33