Respuesta :
let x denote your winnings for a $1 bet, so x = $0 or x = $330. construct the probability distribution for x.
you pick one of the 1000 three-digit numbers between 000 and 999
total number of occurrences = 100
With a single $1 bet, the probability that you win $330 = [tex]\frac{1}{1000}[/tex]
= 0.001
The probability you lose = 1 - probability(win)
= 1- 0.001 = 0.999
Now we make probability distribution table
x P(x)
$0 0.999 (you lost)
$330 0.001 (you win)
The probability of winning the lottery P(x=$330) is 0.001 while the probability of not winning a lottery P(x=0) is 0.999.
What is Probability?
The probability helps us to know the chances of an event occurring.
[tex]\rm{Probability=\dfrac{Desired\ Outcomes}{Total\ Number\ of\ outcomes\ possible}[/tex]
Given to us
A bet of $1, you win $330 if your number is selected and nothing ($0) otherwise.
Select a number between 000 and 999.
We know in order to find the probability we need to know the total number of choices that can be selected. As we can see that the number can be selected from 000 to 999, therefore, there are 1000 outcomes possible.
As we can select only anyone number, therefore, the desired outcome is 1, while the possible outcome is 1000. therefore, the probability of winning the lottery,
[tex]Probability_{(x = \$330)} = \dfrac{Desired\ Outcomes}{Total\ Number\ of\ outcomes\ possible}\\\\P_{(x = \$330)} = \dfrac{1}{1000}[/tex]
We know that the sum of all the probabilities of an event is 1, therefore, the probability that we will not win a lottery,
[tex]Probability_{(x=0)} = 1 - Probability_{(x = \$330)} \\\\P_{(x=0)} = 1 -P_{(x = \$330)}\\\\P_{(x=0)} = 1 -\dfrac{1}{1000}\\\\P_{(x=0)} = \dfrac{999}{1000}[/tex]
Hence, the probability of winning the lottery P(x=$330) is 0.001 while the probability of not winning a lottery P(x=0) is 0.999.
Learn more about Probability:
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