Which event is most likely to occur?
A. Rolling a prime number on a six-sided die, numbered from 1 to 6.
B. Spinning a spinner divided into four equal-sized sections colored red/green/yellow/blue and landing on brown.
C. Winning a raffle that sold a total of 100 tickets, if you buy 82 tickets.
D. Reaching into a bag full of 10 strawberry chews and 10 cherry chews without looking and pulling out a strawberry chew.
A. Rolling a prime number on a six-sided die, numbered from 1 to 6.
In a popular online role playing game, players can create detailed designs for their character's "costumes," or appearance. Justin sets up a website where players can buy and sell these costumes online. Information about the number of people who visited the website and the number of costumes purchased in a single day is listed below.
143 visitors purchased no costume.
26 visitors purchased exactly one costume.
16 visitors purchased more than one costume.
If next week, he is expecting 1400 visitors, about how many would you expect to buy exactly one costume? Round your answer to the nearest whole number.
To find the estimated number of visitors who would buy exactly one costume, we first need to calculate the total number of visitors who bought costumes.
From the information given:
143 visitors purchased no costume.
26 visitors purchased exactly one costume.
16 visitors purchased more than one costume.
Total number of visitors who purchased costumes = 26 (exactly one) + 16 (more than one) = 42
Now, we can find the proportion of visitors who purchased exactly one costume:
Proportion of visitors who bought exactly one costume = Number of visitors who bought exactly one costume / Total visitors who bought costumes
Proportion = 26 / 42 ≈ 0.619
Next, we can use this proportion to estimate the number of visitors who would buy exactly one costume out of 1400 visitors:
Estimated number of visitors who would buy exactly one costume = Proportion * Total visitors expected
Estimated number = 0.619 * 1400 ≈ 866.6
Rounding this to the nearest whole number:
Estimated number of visitors who would buy exactly one costume ≈ 867
Therefore, next week, about 867 visitors would be expected to buy exactly one costume.
David has a bag that contains strawberry chews, apple chews, and watermelon chews. He performs an experiment. David randomly removes a chew from the bag, records the result, and returns the chew to the bag. David performs the experiment 63 times. The results are shown below:
A strawberry chew was selected 35 times.
A apple chew was selected 8 times.
A watermelon chew was selected 20 times.
If the experiment is repeated 1700 more times, about how many times would you expect David to remove a strawberry chew from the bag? Round your answer to the nearest whole number.
To find the estimated number of times David would remove a strawberry chew from the bag when repeating the experiment 1700 more times, we first calculate the proportion of times a strawberry chew was selected in the initial 63 experiments.
From the given results:
- A strawberry chew was selected 35 times.
- A apple chew was selected 8 times.
- A watermelon chew was selected 20 times.
Total number of experiments in the initial 63 trials = 35 (strawberry) + 8 (apple) + 20 (watermelon) = 63
Proportion of times a strawberry chew was selected in the initial trials:
Proportion of selecting a strawberry chew = Number of times a strawberry chew was selected / Total number of experiments
Proportion = 35 / 63 ≈ 0.5556
Now, we will use this proportion to estimate the number of times a strawberry chew would be selected in the additional 1700 experiments:
Estimated number of times a strawberry chew would be selected = Proportion * Total number of additional experiments
Estimated number = 0.5556 * 1700 ≈ 944.52
Rounding this to the nearest whole number:
Estimated number of times a strawberry chew would be selected in the additional experiments ≈ 945
Therefore, when repeating the experiment 1700 more times, you would expect David to remove a strawberry chew from the bag about 945 times.