Suppose that in the city in
which the survey is conducted, 50% of adults are
married, 15% are single, 25% are divorced, and
10% are widowed.
a. Assign probabilities to each simple event in the
sample space.
b. Which approach did you use in part (a)?
Find the probabilities of each of the following events.
a. The adult is single. --> 0.15
b. The adult is not divorced --> 0.75
c. The adult is either widowed or divorced. --> 0.35
Am I right?
correct
a. The probabilities for each simple event in the sample space are as follows:
- Married: 0.50
- Single: 0.15
- Divorced: 0.25
- Widowed: 0.10
b. For part (a), I used the approach of assigning probabilities based on the given information about the percentages of adults in each marital status category.
Regarding your answers to the probabilities of each event:
a. Correct! The probability of an adult being single is 0.15.
b. Correct! The probability of an adult not being divorced is 0.75 (100% - 25%).
c. Incorrect! The probability of an adult being either widowed or divorced is 0.35.
a. The sample space consists of four simple events: married, single, divorced, and widowed. We can assign the following probabilities to each event:
P(married) = 0.50
P(single) = 0.15
P(divorced) = 0.25
P(widowed) = 0.10
b. I used the classical approach in part (a) to assign probabilities to each simple event based on the given information.
The probabilities you provided for each of the events are correct:
a. P(single) = 0.15
b. P(not divorced) = 1 - P(divorced) = 1 - 0.25 = 0.75
c. P(widowed or divorced) = P(widowed) + P(divorced) = 0.10 + 0.25 = 0.35
So, you are right.
a. To assign probabilities to each simple event in the sample space, we need to consider the percentages given for each marital status.
Given percentages:
- 50% of adults are married
- 15% of adults are single
- 25% of adults are divorced
- 10% of adults are widowed
Assigning probabilities to each simple event:
Let's assume the sample space consists of the following simple events:
- A: Married
- B: Single
- C: Divorced
- D: Widowed
The probabilities assigned to each simple event are:
- P(A) = 0.50 (50%)
- P(B) = 0.15 (15%)
- P(C) = 0.25 (25%)
- P(D) = 0.10 (10%)
b. In part (a), we used the approach where we assigned probabilities based on the given percentages. This approach is commonly used when the probabilities of simple events are directly stated or can be calculated from given information.
Now let's verify the probabilities for the events mentioned in part (b):
a. The probability of an adult being single is correctly mentioned as 0.15 (15%).
b. The probability of an adult not being divorced can be calculated by subtracting the probability of being divorced from 1.
Probability of not being divorced = 1 - P(C) = 1 - 0.25 = 0.75 (75%).
c. The probability of an adult being either widowed or divorced can be calculated by adding the probabilities of those two simple events.
Probability of being widowed or divorced = P(C) + P(D) = 0.25 + 0.10 = 0.35 (35%).
Based on the calculations, your answers are correct. Well done!