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
a) The simple events of the experiment are as follows:
1) A kid is 1 year old.
2) A kid is 2 years old.
3) A kid is 3 years old.
4) A kid is 4 years old.
5) A kid is 5 years old.
b) To calculate the probability of each simple event, we divide the number of kids in each age group by the total number of kids:
1) P(A kid is 1 year old) = Number of kids who are 1 year old / Total number of kids
= 3 / (3 + 22 + 8 + 16 + 9)
= 3 / 58
2) P(A kid is 2 years old) = Number of kids who are 2 years old / Total number of kids
= 22 / (3 + 22 + 8 + 16 + 9)
= 22 / 58
3) P(A kid is 3 years old) = Number of kids who are 3 years old / Total number of kids
= 8 / (3 + 22 + 8 + 16 + 9)
= 8 / 58
4) P(A kid is 4 years old) = Number of kids who are 4 years old / Total number of kids
= 16 / (3 + 22 + 8 + 16 + 9)
= 16 / 58
5) P(A kid is 5 years old) = Number of kids who are 5 years old / Total number of kids
= 9 / (3 + 22 + 8 + 16 + 9)
= 9 / 58
c) To calculate the probability of sampling a kid who is at least 2 years old, we need to consider the probabilities of all the age groups from 2 years and above:
P(Sampling a kid who is at least 2 years old) = P(A kid is 2 years old) + P(A kid is 3 years old) + P(A kid is 4 years old) + P(A kid is 5 years old)
= (22 / 58) + (8 / 58) + (16 / 58) + (9 / 58)
d) To calculate the probability of sampling a kid who is 4 years old:
P(Sampling a kid who is 4 years old) = P(A kid is 4 years old)
= 16 / 58
e) To calculate the probability of sampling a kid who is 3 years and younger:
P(Sampling a kid who is 3 years and younger) = P(A kid is 1 year old) + P(A kid is 2 years old) + P(A kid is 3 years old)
= (3 / 58) + (22 / 58) + (8 / 58)
a) The simple events in this experiment are the different age groups of kids that usually play in the park on a Sunday morning. In this case, the simple events are:
- Kids who are 1 year old
- Kids who are 2 years old
- Kids who are 3 years old
- Kids who are 4 years old
- Kids who are 5 years old
b) To find the probability of each simple event, you divide the number of kids in each age group by the total number of kids in the park.
To calculate the probabilities, you need to find the total number of kids in the park. By summing up the number of kids in each age group:
Total number of kids = 3 + 22 + 8 + 16 + 9 = 58
Then, you can find the probability for each age group:
- Probability of kids who are 1 year old = (number of kids who are 1 year old) / (total number of kids) = 3 / 58
- Probability of kids who are 2 years old = (number of kids who are 2 years old) / (total number of kids) = 22 / 58
- Probability of kids who are 3 years old = (number of kids who are 3 years old) / (total number of kids) = 8 / 58
- Probability of kids who are 4 years old = (number of kids who are 4 years old) / (total number of kids) = 16 / 58
- Probability of kids who are 5 years old = (number of kids who are 5 years old) / (total number of kids) = 9 / 58
c) To find the probability of sampling a kid who is at least 2 years old, you need to sum up the probabilities of the age groups that are 2 years old and older.
Probability of sampling a kid who is at least 2 years old = Probability of kids who are 2 years old + Probability of kids who are 3 years old + Probability of kids who are 4 years old + Probability of kids who are 5 years old
= (22/58) + (8/58) + (16/58) + (9/58)
d) To find the probability of sampling a kid who is 4 years old, you simply use the probability of the specific age group.
Probability of sampling a kid who is 4 years old = Probability of kids who are 4 years old = 16/58
e) To find the probability of sampling a kid who is 3 years and younger, you sum up the probabilities of the age groups that are less than or equal to 3 years old.
Probability of sampling a kid who is 3 years and younger = Probability of kids who are 1 year old + Probability of kids who are 2 years old + Probability of kids who are 3 years old
= (3/58) + (22/58) + (8/58)