Question

Find the probability of winning a lottery in which you win when the six numbers on yourticket must match the six unique numbers selected from a set of positive integers not ex-ceeding 30. The order of the numbers on your ticket, do not matter as in order to win, allyou must do is match all the numbers.

Answer 1

Answer:

0.00016841%

Step-by-step explanation:

The winning group of numbers consist of 6 unique number inside a pool of 30 numbers. To calculate the number of groups of 6 that can be done in a pool of 30 numbers, we do a combination of 30 chosen 6 (groups of 6 numbers in 30 numbers).

The formula of combination is:

C(n,p) = n![p!*(n-p)!]

In our case, n=30 and p=6, so we have

C(30,6)=30!/(6!24!) = 30*29*28*27*26*25/(6*5*4*3*2) = 593775

As we have 593775 numbers of different possibilities of winning ticket, the probability of winning one over this value:

p = 1/593775 = 0.0000016841 = 0.00016841%

Other way to do this question is:

We have to match all 6 numbers. The first number to match have a chance of 6 over 30 to be guessed right, as there are 6 winning number in a pool of 30.

The second number to match have a chance of 5 over 29, as we already picked one winning number, and have only 29 choices left.

Then, following this logic, we have the other 4 numbers with chance 4/28, 3/27, 2/26 and 1/25.

Multiplying all these chances, we have:

p = (6*5*4*3*2*1)/(30*29*28*27*26*25) = 0.0000016841 = 0.00016841%