The probability that an automobile being filled with gasoline also needs an oil change is 0.30; the probability that it needs a new oil filter is 0.40; and the probability that both the oil and the filter need changing is 0.10. (a) If the oil has to be changed, what is the probability that a new oil filter is needed? (b) If a new oil filter is needed, what is the probability that the oil has to be changed?
Diabetes and unemployment. A Gallup poll surveyed Americans about their employment status and whether or not they have diabetes. The survey results indicate that 1.5% of the 47,774 employed (full or part time) and 2.5% of the 5,855 unemployed 18-29 year olds have diabetes. (Gallup, 2012)
a. Create a two-way table presenting the results of this study.
b. State appropriate hypotheses to test for difference in proportions of diabetes between employed and unemployed Americans.
c. The sample difference is about 1%. If we completed the hypothesis test, we would find that the p-value is very small (about 0), meaning the difference is statistically significant. Use this result to explain the difference between statistically significant and practically significant findings.
A coin is tossed and a die is rolled, what is the probability of getting head in tossing a coin and getting an odd number when casting a fair die?
3. A vase contains 8 pink, 9 purple, and 11 yellow tulips. You randomly choose a flower from the vase to take home. Your best friend randomly chooses another flower from the vase to take home. What is the probability that you choose pink tulips and your best friend chooses purple tulips?
4. Ace is planning to enroll in short courses in TESDA. He plans to take Bread and Pastry Production, and Food and Beverage Service. The probability of finishing Bread and Pastry Production is 48%, and 53% for Food and Beverage Service. If the probability of finishing both courses is 40%, what is the probability of passing at least one course?
5. According to DOST-FNRI, 24.7% of the population of Filipino elderly, 60 years old and above, are obese. If we select three elderly at random, what is the probability that all selected will be obese?
Another interesting aspect of statistics and probability that you will encounter in high school and at college is dealing with two-way tables, which is less complex than it really is. You can start with the two-way tables math that you will encounter not only with the equations but with the majority of questions that deal with two-way tables math where you have two categories. If this sounds too complex as you are looking for answers, turn to our examples of two-way tables. The safest bet would be starting with the two-way tables answers that will have both calculation and analysis.