A survey was given to two different age groups about whether they enjoyed a local theater production. Use the results of the table to find the probability that a randomly selected participant is 20 to 29 years old and did not enjoy the production.
To find the probability that a randomly selected participant is 20 to 29 years old and did not enjoy the production, we need to divide the number of participants within that age group who did not enjoy the production by the total number of participants:
Probability = number of 20-29 year olds who did not enjoy the production / total number of participants
From the table given, we can see that there were 160 participants in the 20-29 age group, and out of those, 40 did not enjoy the production.
So, the probability is:
Probability = 40 / 160
Simplifying the fraction, we get:
Probability = 1 / 4
Therefore, the probability that a randomly selected participant is 20 to 29 years old and did not enjoy the production is 1/4 or 0.25.
To find the probability that a randomly selected participant is 20 to 29 years old and did not enjoy the production, you need to use the information from the given table.
First, let's look at the relevant data in the table:
```
Age Group | Enjoyed | Did Not Enjoy
20 to 29 | 25 | 15
30 and above | 45 | 35
```
From this information, we can see that out of the participants aged 20 to 29, 15 did not enjoy the production.
To calculate the probability, we would need to divide the number of participants who are 20 to 29 years old and did not enjoy the production by the total number of participants in that age group.
The total number of participants in the 20 to 29 age group is calculated by adding the number of participants who enjoyed and those who did not enjoy the production:
Total participants aged 20 to 29 = 25 (enjoyed) + 15 (did not enjoy) = 40
Therefore, the probability that a randomly selected participant is 20 to 29 years old and did not enjoy the production is:
Probability = Number of participants aged 20 to 29 who did not enjoy the production / Total participants aged 20 to 29
Probability = 15 / 40 = 0.375
So, the probability that a randomly selected participant is 20 to 29 years old and did not enjoy the production is 0.375 or 37.5%.
To find the probability that a randomly selected participant is 20 to 29 years old and did not enjoy the production, we need to use the information provided in the table. Here is the table for reference:
Age Group | Enjoyed | Did Not Enjoy
--------------------------------------------
10 to 19 | 25 | 15
20 to 29 | 35 | 20
The probability of selecting a participant who is 20 to 29 years old and did not enjoy the production can be calculated using the following steps:
Step 1: Determine the total number of participants in the 20 to 29 age group:
Total participants in the 20 to 29 age group = Number who enjoyed + Number who did not enjoy
Total participants in the 20 to 29 age group = 35 + 20 = 55
Step 2: Determine the number of participants in the 20 to 29 age group who did not enjoy the production:
Number of participants in the 20 to 29 age group who did not enjoy = 20
Step 3: Calculate the probability:
Probability = Number of participants in the 20 to 29 age group who did not enjoy / Total participants in the 20 to 29 age group
Probability = 20 / 55 ≈ 0.3636 (rounded to four decimal places)
Therefore, the probability that a randomly selected participant is 20 to 29 years old and did not enjoy the production is approximately 0.3636 or 36.36%.