In a lottery, you have to select a three-digit number such as 123. During the drawing, there are
three bins, each containing balls numbered 1 through 9. One ball is drawn from each bin to form
the three-digit winning number.
i. You purchase one ticket with one three-digit number. What is the probability that you will
win this lottery?
ii. There are many variations of this lottery. The primary variation allows you to win if the
three digits in your number are selected in any order as long as they are the same three digits
as obtained by the lottery agency. For example, if you pick three digits making the number
123, then you will win if 123, 132, 213, 231, and so forth, are drawn. The variations of the
lottery game depend on how many unique digits are in your number. Consider the following
two different versions of this game. Find the probability that you will win this lottery in
each of these two situations.
a. All three digits are unique (e.g., 123)
b. Exactly one of the digits appears twice (e.g., 122 or 121)
Answers
Answer:
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Given : In a lottery, you have to select a three-digit number such as 123. During the drawing, there are
three bins, each containing balls numbered 1 through 9.
To Find :
probability that you will win this lottery in each of these two situations.
a. All three digits are unique (e.g., 123)
b. Exactly one of the digits appears twice (e.g., 122 or 121)
Solution:
Probability of winning when order is fixed = (1/9)³ = 1/729
Probability of winning when order is not fixed
All three digits are unique that 3 digits can be arranged in 3! = 6 ways
Probability = 6/729 = 2/243
Exactly one of the digits appears twice Hence these can be arranged in 3!/2! = 3 ways
Probability = 3/729 = 1/243
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