# A statistical investigation showed that adults in a particular country have an 80% chance of living to be at least 70 years old and a 50% chance of living to be at least 80 years old. What is the probability that an adult who just turned 70 will live to be 80?

Question
Probability
A statistical investigation showed that adults in a particular country have an 80% chance of living to be at least 70 years old and a 50% chance of living to be at least 80 years old. What is the probability that an adult who just turned 70 will live to be 80?

2021-03-13
The probability of living to be at least 80 years old is dependent on the probability of living to be at least 70 years old since a person can't live to be at least 80 years old if they did not live to be at least 70 years old.
The formula for two dependent events A and B is P(A and B)=P(A)⋅P(B∣A).
Let AA be the probability that a person lives to be at least 70 years old and BB be the probability that a person lives to be at least 80 years old. You then need to find P(B∣A) since you need to find the probability that a person will live to be at least 80 years old given that they have already lived to be 70 years old. It is given that the probability of living to be at least 70 years old is 80% so P(A)=0.8. It is also given that the probability of living to be at least 80 years old is 50% so P(A and B)=0.5. Therefore:
P(A and B)=P(A)⋅P(B∣A)
0.5=0.8⋅P(B∣A)
0.5/0.8=P(B∣A)
0.625=P(B∣A)
The probability that a person will live to be at least 80 years old given that they have just turned 70 years old is then 0.625=62.5%.

### Relevant Questions

The table below shows the number of people for three different race groups who were shot by police that were either armed or unarmed. These values are very close to the exact numbers. They have been changed slightly for each student to get a unique problem.
Suspect was Armed:
Black - 543
White - 1176
Hispanic - 378
Total - 2097
Suspect was unarmed:
Black - 60
White - 67
Hispanic - 38
Total - 165
Total:
Black - 603
White - 1243
Hispanic - 416
Total - 2262
Give your answer as a decimal to at least three decimal places.
a) What percent are Black?
b) What percent are Unarmed?
c) In order for two variables to be Independent of each other, the P $$(A and B) = P(A) \cdot P(B) P(A and B) = P(A) \cdot P(B).$$
This just means that the percentage of times that both things happen equals the individual percentages multiplied together (Only if they are Independent of each other).
Therefore, if a person's race is independent of whether they were killed being unarmed then the percentage of black people that are killed while being unarmed should equal the percentage of blacks times the percentage of Unarmed. Let's check this. Multiply your answer to part a (percentage of blacks) by your answer to part b (percentage of unarmed).
Remember, the previous answer is only correct if the variables are Independent.
d) Now let's get the real percent that are Black and Unarmed by using the table?
If answer c is "significantly different" than answer d, then that means that there could be a different percentage of unarmed people being shot based on race. We will check this out later in the course.
Let's compare the percentage of unarmed shot for each race.
e) What percent are White and Unarmed?
f) What percent are Hispanic and Unarmed?
If you compare answers d, e and f it shows the highest percentage of unarmed people being shot is most likely white.
Why is that?
This is because there are more white people in the United States than any other race and therefore there are likely to be more white people in the table. Since there are more white people in the table, there most likely would be more white and unarmed people shot by police than any other race. This pulls the percentage of white and unarmed up. In addition, there most likely would be more white and armed shot by police. All the percentages for white people would be higher, because there are more white people. For example, the table contains very few Hispanic people, and the percentage of people in the table that were Hispanic and unarmed is the lowest percentage.
Think of it this way. If you went to a college that was 90% female and 10% male, then females would most likely have the highest percentage of A grades. They would also most likely have the highest percentage of B, C, D and F grades
The correct way to compare is "conditional probability". Conditional probability is getting the probability of something happening, given we are dealing with just the people in a particular group.
g) What percent of blacks shot and killed by police were unarmed?
h) What percent of whites shot and killed by police were unarmed?
i) What percent of Hispanics shot and killed by police were unarmed?
You can see by the answers to part g and h, that the percentage of blacks that were unarmed and killed by police is approximately twice that of whites that were unarmed and killed by police.
j) Why do you believe this is happening?
Do a search on the internet for reasons why blacks are more likely to be killed by police. Read a few articles on the topic. Write your response using the articles as references. Give the websites used in your response. Your answer should be several sentences long with at least one website listed. This part of this problem will be graded after the due date.
Fruit Flles An experiment with fruit flies involves one parent with notmal wings and ooe parent with vestigial wings. When these parents have an of$$\displaystyle\frac{{3}}{{4}}$$ probabulty that the of$$\displaystyle\frac{{1}}{{4}}/{4}$$ probability of vestigial wings. If the parents give birth to five of See answers (1)
Census reports for a city indicate that 62% of residents classify themselves as Christian, 12% as Jewish , and 16% as members of other religions (Muslims, Buddhists, etc.).
The remaining residents classify themselves as nonreligious.
A polling organization seeking information about public opinions wants to be sure to talk with people holding a variety of religious views, and makes random phone calls. Among the first four people they call, what is the probability they reach a) all Christians? b) no Jews? c) at least one person who is nonreligious?
A bipolar alkaline water electrolyzer stack module comprises 160 electrolytic cells that have an effective cell area of $$\displaystyle{2}{m}^{{2}}$$. At nominal operation, the current density for a single cell of the electrolyzer stack is 0.40 $$\displaystyle\frac{{A}}{{c}}{m}^{{2}}$$. The nominal operating temperature of the water electrolyzer stack is $$\displaystyle{70}^{\circ}$$ C and pressure 1 bar. The voltage over a single electrolytic cell is 1.96 V at nominal load and 1.78 V at 50% of nominal load. The Faraday efficiency of the water electrolyzer stack is 95% at nominal current density, but at 50% of nominal load, the Faraday efficiency decreases to 80%.
Calculate the nominal stack voltage:
Calculate the nominal stack current:
Calculate the nominal power on the water electrolyzer stack:
The presidential election is coming. Five survey companies (A, B, C, D, and E) are doing survey to forecast whether or not the Republican candidate will win the election. Each company randomly selects a sample size between 1000 and 1500 people. All of these five companies interview people over the phone during Tuesday and Wednesday. The interviewee will be asked if he or she is 18 years old or above and U.S. citizen who are registered to vote. If yes, the interviewee will be further asked: will you vote for the Republican candidate? On Thursday morning, these five companies announce their survey sample and results at the same time on the newspapers. The results show that a% (from A), b% (from B), c% (from C), d% (from D), and e% (from E) will support the Republican candidate. The margin of error is plus/minus 3% for all results. Suppose that $$\displaystyle{c}{>}{a}{>}{d}{>}{e}{>}{b}$$. When you see these results from the newspapers, can you exactly identify which result(s) is (are) not reliable and not accurate? That is, can you identify which estimation interval(s) does (do) not include the true population proportion? If you can, explain why you can, if no, explain why you cannot and what information you need to identify. Discuss and explain your reasons. You must provide your statistical analysis and reasons.
Data is being processed from 35 data sources. Each dataset may or may or net generate dataset at the beginning of each timeslot, the probability that any individual source actually generates a dataset is 0.004,and the data sources are independent. In each time slot we can process up to two datasets. Now, the processing is real time with the processed results only being considered if they are done within the time slot. Determine the probability that all incoming datasets can be processed in any particular time slot?
Three students are arguing, Chad says, "I think the probability is 1 out of 2." Tien says, "No, it is 40 over 80." Falicia says, "It is 50%." What do you say to the students?
A survey of 4826 randomly selected young adults (aged 19 to 25 ) asked, "What do you think are the chances you will have much more than a middle-class income at age 30? The two-way table summarizes the responses.
$$\begin{array} {c|cc|c} & \text { Female } & \text { Male } & \text { Total } \\ \hline \text { Almost no chance } & 96 & 98 & 194 \\ \hline \text { Some chance but probably not } & 426 & 286 & 712 \\ \hline \text { A 50-50 chance } & 696 & 720 & 1416 \\ \hline \text { A good chance } & 663 & 758 & 1421 \\ \hline \text { Almost certain } & 486 & 597 & 1083 \\ \hline \text { Total } & 2367 & 2459 & 4826 \end{array}$$
Choose a survey respondent at random. Define events G: a good chance, M: male, and N: almost no chance. Given that the chosen student didn't say "almost no chance," what's the probability that this person is female? Write your answer as a probability statement using correct symbols for the events.
It is estimated that aproximately $$\displaystyle{8.36}\%$$ Americans are afflicted with Diabetes .
Suppose that a ceratin diagnostic evaluation for diabetes will correctly diagnose $$\displaystyle{94.5}\%$$ of all adults over 40 with diabetes as having the disease and incorrectly diagnoses $$\displaystyle{2}\%$$ of all adults over 40 without diabetes as having the disease .
1) Find the probability that a randamly selected adult over 40 doesn't have diabetes and is diagnosed as having diabetes ( such diagnoses are called "false positives").
2) Find the probability that a randomly selected adult of 40 is diagnosed as not having diabetes.
3) Find the probability that a randomly selected adult over 40 actually has diabetes , given that he/she is diagnosed as not having diabetes (such diagnoses are called "false negatives").
Note: It will be helpful to first draw an appropriate tree diagram modeling the situation.