A study was conducted to count the different age groups of kids that usually play in a park on a Sunday morning. The following data was collected
Years Old Number of Kids
1 3
2 22
3 8
4 16
5 9
a) List the simple events of the experiment.
b) What is the probability of each simple event?
c) What is the probability of sampling a kid who is at least 2 years old?
d) What is the probability of sampling a kid who is 4 years old?
e) What is the probability of sampling a kid who is 3 years and younger
To answer these questions, we need to understand the basic concepts of probability and how to calculate it using the given data.
a) The simple events are the different possible outcomes of the experiment. In this case, the simple events are the different age groups of kids that usually play in the park on a Sunday morning. So, the simple events in this study are: 1 year old, 2 years old, 3 years old, 4 years old, and 5 years old.
b) To calculate the probability of each simple event, we need to divide the number of kids in each age group by the total number of kids. Let's calculate it:
- Probability of a 1-year-old kid: Divide the number of 1-year-old kids (3) by the total number of kids (3 + 22 + 8 + 16 + 9 = 58). So, the probability is 3/58.
- Probability of a 2-year-old kid: Divide the number of 2-year-old kids (22) by the total number of kids (58). So, the probability is 22/58 (which can be simplified to 11/29).
- Probability of a 3-year-old kid: Divide the number of 3-year-old kids (8) by the total number of kids (58). So, the probability is 8/58 (which can be simplified to 4/29).
- Probability of a 4-year-old kid: Divide the number of 4-year-old kids (16) by the total number of kids (58). So, the probability is 16/58 (which can be simplified to 8/29).
- Probability of a 5-year-old kid: Divide the number of 5-year-old kids (9) by the total number of kids (58). So, the probability is 9/58.
c) To calculate the probability of sampling a kid who is at least 2 years old, we need to add the probabilities of sampling a 2-year-old kid, a 3-year-old kid, a 4-year-old kid, and a 5-year-old kid. Let's calculate it:
- Probability of a kid at least 2 years old = Probability of a 2-year-old kid + Probability of a 3-year-old kid + Probability of a 4-year-old kid + Probability of a 5-year-old kid
So, it would be (22/58) + (8/58) + (16/58) + (9/58), which simplifies to 55/58.
d) To calculate the probability of sampling a kid who is 4 years old, we divide the number of 4-year-old kids (16) by the total number of kids (58). So, the probability is 16/58 (which can be simplified to 8/29).
e) To calculate the probability of sampling a kid who is 3 years and younger, we need to add the probabilities of sampling a 1-year-old kid, a 2-year-old kid, and a 3-year-old kid. Let's calculate it:
- Probability of a kid who is 3 years and younger = Probability of a 1-year-old kid + Probability of a 2-year-old kid + Probability of a 3-year-old kid
So, it would be (3/58) + (22/58) + (8/58), which simplifies to 33/58.