Question

1) In the game Super Vegas Lottery, four digits are drawn at random one at a
time with replacement from 0 to 9.
In other words, there are 10 slips of paper in a jar, each with a di erent digit printed
on it. A slip is drawn from the jar, the number written down, then the slip is put back

into the jar, and the jar is shaken up. This process is repeated three more times.
You win if any permutation of your numbers is drawn. What is the probability that
you win if your numbers are:
(a) 6, 7, 8, 9
(b) 6, 7, 8, 8
(c) 7, 7, 8, 8
(d) 7, 8, 8, 8
Hint: How many outcomes are there in the outcome space? That is, how many four-
digit permutations can be drawn from the jar? Each of these outcomes is equally likely.
Consider your four digits. How many di erent permutations can be formed from your
four digits? Use this information to calculate the probability of winning.

Answer 1

a)

There are 10*10*10*10 = 10000 possibilities.

As this is 4! = 24 permutations, then

P(win) = 24/10000 = 0.0024 [ANSWER]

b)

By permutation of like objects, this has

4!/(1!1!2!) = 12 permutations. Hence,

P(win) = 12/10000 = 0.0012 [ANSWER]

c)

By permutation of like objects, this has

4!/(2!2!) = 6 permutations. Hence,

P(win) = 6/10000 = 0.0006 [ANSWER]

d)

By permutation of like objects, this has

4!/(1!3!) = 4 permutations. Hence,

P(win)= 4/10000 = 0.0004 [ANSWER]