Question

37. Most states run a lottery game in which players may select a three-digit number using the digits 0,1,2,3,4,5,6,7,8,9 with repetition allowed and then later that day a televised drawing randomly selects a winning three-digit number. a. How many outcomes are in the sample space? 1000 3 300 100 b. Suppose you select one three-digit number and buy a ticket. What is the probability that your three-digit number is an exact match with the winning three-digit number? 1/2 1/1000 1/3 1/10 c. "Expected winnings" is defined as the prize money for winning the game multiplied by the probability of winning the game. In this state lottery game, what would be your expected winnings if the prize is $1000? $1000 $100 $10 $1

          37. Most states run a lottery game in which players may select a three-digit number using the digits 0,1,2,3,4,5,6,7,8,9 with repetition allowed and then later that day a televised drawing randomly selects a winning three-digit number.

a. How many outcomes are in the sample space?
1000
3
300
100

b. Suppose you select one three-digit number and buy a ticket. What is the probability that your three-digit number is an exact match with the winning three-digit number?
1/2
1/1000
1/3
1/10

c. "Expected winnings" is defined as the prize money for winning the game multiplied by the probability of winning the game. In this state lottery game, what would be your expected winnings if the prize is $1000?
$1000
$100
$10
$1

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37. Most states run a lottery game in which players may select a three-digit number using the digits 0,1,2,3,4,5,6,7,8,9 with repetition allowed and then later that day a televised drawing randomly selects a winning three-digit number.

a. How many outcomes are in the sample space?
1000
3
300
100

b. Suppose you select one three-digit number and buy a ticket. What is the probability that your three-digit number is an exact match with the winning three-digit number?
1/2
1/1000
1/3
1/10

c. "Expected winnings" is defined as the prize money for winning the game multiplied by the probability of winning the game. In this state lottery game, what would be your expected winnings if the prize is 1000?1000
10010
1

Added by Joshua N.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

Instant Answer

Solved by Expert Joanna Quigley

07/18/2022

Step 1

Since there are 10 digits (0-9) and repetition is allowed, there are 10 choices for each of the three digits. So, the total number of outcomes in the sample space is: $10 \times 10 \times 10 = 1000$ Now, let's find the probability of an exact match. Since there Show more…

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Most states run a lottery game in which players may select a three-digit number using the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 with repetition allowed and then later that day a televised drawing randomly selects a winning three-digit number. a. How many outcomes are in the sample space? 1000 b. Suppose you select one three-digit number and buy a ticket. What is the probability that your three-digit number is an exact match with the winning three-digit number? 1/1000 c. "Expected winnings" is defined as the prize money for winning the game multiplied by the probability of winning the game. In this state lottery game, what would be your expected winnings if the prize is $1000? $1

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Transcript

00:01 We're looking at a lottery.

00:03 You pick three numbers, and you can choose any number from 0 -000 to 999.

00:09 First question is how many possible numbers can you choose? well, it's going to be 1 ,000.

00:15 You get three digits.

00:17 Each digit is 0 to 9, so you have 10 possibilities.

00:21 10 from the 1st times 10 times 10 is 1 ,000 different possibilities.

00:28 Part b, if all three -digit numbers are equally likely, what's your probability of winning? so you pick one of the numbers out of a thousand, which means that your chance of winning the exact number is one in a thousand.

00:46 Let's see.

00:47 You pick 156 and you can win if you have the correct three digits.

00:55 So now we make things a bit more complicated.

01:00 So we have 1 .56 and you will win if the correct answer is 1 .5.

01:05 But you will also win if it's 516, you will also win if it's 615, and so on.

01:20 So now the question is how many different ways are there of putting these three digits in order? and we can work that out by saying, okay, i have three digits.

01:32 For my first digit, i have three options.

01:36 This could be a one or a five or a six.

01:38 For my second digit, i only have two options left.

01:42 Let's say the first one is a one, this can now only be a five or a six...

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