Question

Winning the jackpot in a particular lottery requires that you select the correct five numbers between 1 and 34 ​and, in a separate​ drawing, you must also select the correct single number between 1 and 37. Find the probability of winning the jackpot.

Answer 1

The probability of winning the lottery is $\frac{1}{10,295,472}$

Step-by-step explanation:

Here, the total numbers in the jackpot = 1 to 34

Now, the number that needed to be drawn = 5

The number of ways , 5 number can be drawn from total 34 numbers :

$^{34} C _5 = \frac{34!}{5!(34-5)!} = 278,256$

Also, in separate draw, the correct number drawn  = 1

So, the number of ways that can be done  =  30 C 5 x  37  

= 278,256 x 37    = 10,295,472

Now, P(win)   =  $\frac{\textrm{Total favorable attempts}}{\textrm{Total attempts}} = \frac{1}{10,295,472}$

Hence, the probability of winning the lottery is $\frac{1}{10,295,472}$