Survey Question: Do you like winter?
Survey Results
| Gender | Yes | No | Total |
|---|---|---|---|
| Male | 15 | 25 | 40 |
| Female | 10 | 50 | 60 |
| Total | 25 | 75 | 100 |
Sample question: “Find the probability that the answer was no, given that the respondent was male.”
- Step 1: Find the probability of both the events in the question happening together. In our sample, question, we were asked for the probability of no + male. From the table, that is 25.
- Step 2: Divide your answer in step 1 by the total figure. In our example, it’s a survey, so we need the total number of respondents (100, from the table).
25 / 100 = 0.25 - Step 3: Identify which event happened first (i.e. find the independent variable). In our example, we identified the male subgroup and then we deduced how many answered no, so “total number of males” is the independent event. The question usually gives this information away by telling you “given that the respondents were male…” (as in our question).
- Step 4: Find the probability of the event in Step 3. In our example, we want the probability of being a male in the survey. There are 40 males in our survey, and 100 people total, so the probability of being a male in the survey is 40 / 100, or .4.
- Step 5: Divide the figure you found in step 2 by the figure you found in step 4.
- .25 / .4 = 0.625
Questions:
1.) Use the sample chart to find the probability of females who answered yes.
2.) Find the probability if there was 20 females who answered no.
3.) Find the probability if there was 53 males who answered no.
Answers:
1. Probability for females who answered yes is .4166666
2. Probability for females who answered no is .33333
3. Probability for males who answered no is 1.325
Probability in Real World:
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