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?

win $5,000: P = 0.0006437

win $50: P = 0.6196

Step-by-step 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