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
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. One ball is drawn from each bin to form the three-digit winning number.
To Find : You purchase one ticket with one three-digit number. What is the probability that you will win this lottery?
All three digits are unique
Solution :
There are three digits in lottery and each is unique
Order of getting digit form bin can be any :
Probability of getting correct digit from 1st bin = 3/9
as there are three different digit
Now after that only 2 digits left
Hence
Probability of getting correct digit from 2nd bin = 2/9
as now only 1 digit left from the lottery
=> Probability of getting correct digit from 3rd bin = 1/9
Probability of winning = (3/9) (2/9) (1/9)
= 2/243
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Answer:
Step-by-step explanation:
“Probability played a role in the rigging of the April 24,1980 , Pennsylvania state lottery (Los Angeles Times, September 8,1980 ). To determine each digit of the three-digit winning number. each of the numbers 0,1,2,…,9
is placed on a Ping-Pong ball. the ten balls are blown into a compartment, and the number selected for the digit is the one on the ball that floats to the top of the machine. To alter the odds, the conspirators injected a liquid into all balls used in the game except those numbered 4 and 6,
making it almost certain that the lighter balls would be selected and determine the digits in the winning number. Then they bought lottery tickets bearing the potential winning numbers. How many potential winning numbers were there (666 was the eventual winner)”