Question

In a state lottery 25 balls numbered from 1 to 25 and placed in machine. 6 numbers randomly drawn. And here is the chart what can win a player by buying single lottery ticket:

6 number match $10,000
5 number match $ 5,000
4 number match $ 1000
3 number match $ 5,00
2 number match $ 50
1 number match $ 10
What is probability that player will win $5,000? What is probability to win $50 ?

Answer 1

For $50: 0.328289102

Explanation:

Using a similar approach to the previous answer, which is really good and helpful (go there if you want the actual explanation!)

Just found a typo in the answer to the second part. You need to discount the right answers when considering the possibilities for the wrong answers, so the final answer will wind up looking like this:

15 * (6/25) * (5/24) * (19/23) * (18/22) * (17/21) * (16/20)

15*6*5*19*18*17*16 = 41860800

25*24*23*22*21*20 = 127512000

Answer = 0.328289102

Answer 2

win $5,000: P = 0.0006437

win $50: P = 0.6196

Explanation:

To win $5,000, we must have a match of 5 numbers.

So from the 6 numbers, we correcly choose 5 numbers and miss 1 number. The probability of matching or not each of the 6 numbers is:

First number: P = 6/25

Second number: P = 5/24

Third number: P = 4/23

Fourth number: P = 3/22

Fifth number: P = 2/21

Sixth number: P = 19/20 (wrong number)

As the 5 correct numbers can be any of the 6, we also have to multiply the probabilities by a combination of 6 choose 5:

c(6,5) = 6!/5! = 6

So the final probability is:

P = 6 * (6/25) * (5/24) * (4/23) * (3/22) * (2/21) * (19/20) = 0.0006437

To find the probability of winning $50, we can do the same steps above, and we need to correcly match 2 numbers, so we have that:

First number: P = 6/25

Second number: P = 5/24

Third number: P = 22/23 (wrong number)

Fourth number: P = 21/22 (wrong number)

Fifth number: P = 20/21 (wrong number)

Sixth number: P = 19/20 (wrong number)

As the 2 correct numbers can be any of the 6, we also have to multiply the probabilities by a combination of 6 choose 2:

c(6,2) = 6!/(4!*2!) = 6*5/2 = 15

So the final probability is:

P = 15 * (6/25) * (5/24) * (22/23) * (21/22) * (20/21) * (19/20) = 0.6196