Question

Winning the jackpot in a particular lottery requires that you select the correct two numbers between 1 and 52 ​and, in a separate​ drawing, you must also select the correct single number between 1 and 35. Find the probability of winning the jackpot.

Answer 1

since there are exactly 2 correct numbers out of 1 to 52 so we can select 2 numbers in ⁵²C₂ =1326 ways

in the second drawing, we have to select 1 correct number we can select 1 number in ³⁵C₁ =35ways

so Prob of selecting 2 correct number =1/1326

Prob of selecting 1 correct number =1/35

since for winning jackpot we need to get 2 correct numbers as well as correct single number

since both drawings are independent

so

Prob (winning jackpot)=1/1326* 1/35 = 1/46410

=0.000021547