Teresa has a copy of her school's student directory on her desk.
Students whose last names start with the letters A to F occupy the first 2 pages of the book.
Students whose last names start with the letters G to M occupy the next 4 pages of the book.
Students whose last names start with the letters N to R occupy the following 10 pages of the book.
Students whose last names start with the letters S to Z occupy the final 9 pages of the book.
If she opens up the directory and picks out a student at random, what is the probability that she selects a page where a student's last name begins with a letter from the first half of the alphabet?
A. 19/25
B. 4/25
C. 2/5
D. 6/25
Let x be the total number of candies without nuts in the box.
Since there are 3 times as many candies with nuts as candies without nuts, the total number of candies with nuts is 3x.
The total number of candies in the box is x (candies without nuts) + 3x (candies with nuts) = 4x.
The probability that Johnny pulled out a candy without nuts is the number of candies without nuts divided by the total number of candies, which is x/4x = 1/4.
Therefore, the correct answer is:
D. 1/4
In a box of candy, there are 3 times as many candies with nuts as candies without nuts. Johnny pulls a candy out of the box at random.
What is the probability that Johnny pulled out a candy without nuts?
A. 3/4
B. 1/5
C. 1/3
D. 1/4
Gretta has a bag of 15 marbles, including 5 blue, 4 red, and 6 black. When reaching into the bag, she expects to select a blue marble of the time.
After selecting a marble and replacing it, she repeats this process six times and records the results below.
Which statement best explains why the results of her experiment did not match her expectations?
A. She performed too many trials.
B. She did not perform enough trials.
C. She should not have replaced the marbles between trials.
D. She really should not be able to draw a blue marble of the time.
The probability of drawing a blue marble is given as 1/3. This means that out of every 3 marbles drawn, 1 is expected to be blue. In other words, if Gretta draws 9 marbles, she is expected to get 3 blue marbles.
Since Gretta repeated the process six times (for a total of 6 x 9 = 54 marbles drawn), she is expected to get 1/3 x 54 = 18 blue marbles.
If Gretta did not get close to 18 blue marbles, it is likely that this discrepancy is due to the random nature of the process, even though the theoretical probability suggests that she should get close to that value. The law of large numbers states that as the number of trials increases, the experimental results should approximate the theoretical probability, but this does not guarantee that the exact results will match every time.
Therefore, the best explanation for the results not matching Gretta's expectations is:
A. She performed too many trials.
This indicates that the discrepancy may be due to the random nature of the process, and performing more trials does not necessarily guarantee an exact match to the expected probabilities.
Eden spun the above spinner 12 times, and recorded the results in the table below.
What is the experimental probability of spinning a 4?
A. 1/12
B. 1/4
C. 1/3
D. 1/10
Since Eden spun the spinner 12 times and recorded the results, we can calculate the experimental probability of spinning a 4 by looking at how many times a 4 came up in the 12 spins.
Looking at the table below, the number "4" came up 3 times out of the 12 spins:
| Spin 1 | Spin 2 | Spin 3 | Spin 4 | Spin 5 | Spin 6 | Spin 7 | Spin 8 | Spin 9 | Spin 10 | Spin 11 | Spin 12 |
|--------|--------|--------|--------|--------|--------|--------|--------|--------|---------|---------|---------|
| 2 | 1 | 4 | 2 | 3 | 4 | 2 | 4 | 3 | 2 | 1 | 2 |
Therefore, the experimental probability of spinning a 4 is 3 (number of times a 4 came up) out of 12 (total number of spins), which simplifies to 1/4.
Therefore, the correct answer is:
B. 1/4
Seth and Chris are pulling cards from a deck of hearts, numbered 1(Ace) through 5. Their results are listed below.
Whose experimental probability is closer to the theoretical probability of pulling out a card with an even number on it?
A. Neither
B. Chris
C. Seth
D. They are about the same.
Danny's office ordered a sandwich tray for lunch. The tray had 4 turkey sandwiches, 6 ham sandwiches, and 5 tuna sandwiches. If Danny randomly picked a sandwich off the tray without looking, what is the probability that he picked a ham sandwich?
A. 1/3
B. 2/5
C. 1/6
D. 3/5
The total number of sandwiches on the tray is 4 (turkey) + 6 (ham) + 5 (tuna) = 15 sandwiches.
The probability of picking a ham sandwich is the number of ham sandwiches divided by the total number of sandwiches:
6 (ham sandwiches) / 15 (total sandwiches) = 2/5.
Therefore, the probability that Danny picked a ham sandwich is:
B. 2/5
To calculate the probability that she selects a page where a student's last name begins with a letter from the first half of the alphabet, we need to determine the total number of pages in the directory and the number of pages that meet the criteria.
There are a total of 2 + 4 + 10 + 9 = 25 pages in the directory.
The number of pages with student last names starting with A to M is 2 + 4 = 6.
Therefore, the probability that Teresa selects a page where a student's last name begins with a letter from the first half of the alphabet is 6/25, which simplifies to 2/5.
Therefore, the correct answer is:
C. 2/5