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?
Answers
Answer:
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Explanation:
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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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