Question

Winning the jackpot in a particular lottery requires that you select the correct four numbers between 1 and 46 and, in a separate​ drawing, you must also select the correct single number between 1 and 28. Find the probability of winning the jackpot.

Answer 1

Here we have

given

Winning the jackpot is 4 numbers between 1 and 46 and, in a separate drawing and the must be correct single number between 1 and 28

4 numbers out of 1 to 46 so we can select 4 numbers in 46C4 ways

in the second drawing, we have to select 1 correct number we can select 1 number in 28C₁ ways

Probability of selecting 4 correct number =1/46C4

Probability of selecting 1 correct number =1/28C₁

since for winning jackpot we need to get 4 correct numbers as well as correct single number

since both drawings are independent

so

Prob (winning jackpot)=(1/46C4) *(1/28C₁ )=(1/163185)*(1/28) =0.000000219