The probability of winning a game is 20%. If you play 20 times, how many times should you expect to win?
We can use proportionality to predict how many of the 800 diners at the restaurant are likely to order an appetizer, based on the proportion observed in the sample.
We can start by writing a proportion between the number of diners who ordered an appetizer in the sample and the total number of diners in the sample, and the number of diners who are likely to order an appetizer in the population and the total number of diners in the population:
12/60 = x/800
To solve for x, we can cross-multiply and simplify:
12 x 800 = 60 x x
9600 = 60x
x = 160
Therefore, we can predict that about 160 diners at the restaurant are likely to order an appetizer each day, based on the sample data.
You can expect to win 4 times.
Explanation:
The probability of winning a game is 20%, or 0.2 as a decimal. This means that out of 100 games, you would expect to win 20.
If you play 20 times, you can think of each game as a separate event with a 20% chance of winning. To find the expected number of wins, you multiply the number of trials (20) by the probability of winning (0.2):
20 x 0.2 = 4
Therefore, you can expect to win 4 times if you play 20 games.
The probability of having a winning raffle ticket is 15%. If you bought 40 tickets, how many winning tickets should you expect to have?
You should expect to have 6 winning tickets.
Explanation:
The probability of winning a raffle ticket is 15%, or 0.15 as a decimal. This means that out of 100 tickets, you would expect to have 15 winning tickets.
If you bought 40 tickets, you can think of each ticket as a separate event with a 15% chance of winning. To find the expected number of winning tickets, you multiply the number of tickets (40) by the probability of winning (0.15):
40 x 0.15 = 6
Therefore, you should expect to have 6 winning tickets if you bought 40 tickets.
A survey of a random sample of moviegoers shows that 40% purchase popcorn to eat while watching the movie. If a theater has 80 people in it, how many people should you expect to have purchased popcorn?
You should expect 32 people to purchase popcorn.
Explanation:
If a survey of a random sample of moviegoers shows that 40% purchase popcorn, this means that out of 100 moviegoers, 40 would purchase popcorn.
Therefore, if a theater has 80 people in it, you can expect the number of people who purchase popcorn to be:
80 x 0.40 = 32
Therefore, you should expect 32 people to purchase popcorn out of 80 people in the movie theater.
A manufacturer finds that 10% of the flashlights in a sample are defective. Predict how many defective flashlights there will be in a shipment of 4,000 flashlights.
There will be 400 defective flashlights in a shipment of 4,000 flashlights.
Explanation:
If 10% of the flashlights in a sample are defective, this means that out of 100 flashlights, 10 will be defective.
Therefore, if a shipment of 4,000 flashlights is expected, the number of defective flashlights can be predicted as:
4,000 x 0.10 = 400
Therefore, there will be 400 defective flashlights in a shipment of 4,000 flashlights.
In a random sample of 30 sixth graders, 9 had traveled outside of the United States. There are a total of 120 sixth graders in the school. Predict how many students have traveled outside of the United States.
There will be about 36 students (or 30% of the 120 sixth graders) who have traveled outside of the United States.
Explanation:
In a random sample of 30 sixth graders, 9 had traveled outside of the United States. This means that 30% (or 9/30) of that particular sample had traveled outside of the United States.
To predict how many sixth graders in the school have traveled outside of the United States, we can use this percentage and apply it to the total number of sixth graders in the school:
120 x 0.30 = 36
Therefore, there will be about 36 sixth graders in the school who have traveled outside of the United States.