Question

In the SmallState Lottery, three white balls are drawn (at random) from twenty balls numbered 1 through 20, and a blue SuperBall is drawn (at random) from ten balls numbered 21 through 30. When you buy a ticket, you select three numbers from 1-20 and one number from 21-30. To win the jackpot, the numbers on your ticket must match the three white balls and the SuperBall. (You don't need to match the white balls in order).

If you buy a ticket, what is your probability of winning the jackpot?

Answer 1

hey this problem is a little urgent. could someone help me answer this? Thanks so much guys!

Answer 2

Probability = number favorable / number total
Lets say the winning ticket numbers are 1,3,19 and 29 . There is only one way to win this particular combination. So the number of favorable ways is 1.
That will be the numerator.
For the denominator we want total number of ways of picking the 3 white balls and 1 blue ball. The total number of ways to draw the three white balls in no particular order is 20 choose 3. Then you draw a blue ball, the total number of ways to get the blue ball is 10 choose 1.
Now you have to multiply these, because they happen in succession.
$$ \Large \rm
P(winning) = \Large {
\frac{1}{{20 \choose 3} {10 \choose 1 }}

}
$$

Answer 3

@dan815 @amistre64 anybody want to look this over

Answer 4

assuing no repetition

20*19*18 ways to pull out 3 white balls, and 9 ways to pull the other ball

there are 6 ways to arrange 3 winning balls, and 1 way to arrange the blue ball

\[\frac{6}{20(19)(18)(9)}\]

my thought process is prolly off, but its 9C1 at best

Answer 5

lets say theres 5w and 2b

abcde xy

5.4.3.2 = 120 ways to pull an outcome in any order

assume abcy is the winner

6 ways to arrange abc, and 1 way to arrange y

abc y
acb y
bac y
bca y
cab y
cba y

6 winning combos out out 120 to choose from in this scenario