Math, asked by iotoobaibuke, 2 months ago

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

Answered by rnrelectricals
0

Answer:

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Answered by amitnrw
0

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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