Answer:
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
