conditional probabilities

Project description
Use Bayes Formula shown in the textbook. This formula uses conditional probabilities, which are covered in the section entitled Bayes Formula.
Lastly, you should study the examples in this section of the textbook before working the three assigned problems. If you have trouble understanding the examples ,

contact your instructor for help.
The answers to the problems are probabilities, which must be between 0 (cant happen) and 1 (must happen).

#1. Credit Unions whose deposits are insured by the National Credit Union Association are classified into three categories: those with fewer than 25,000 members, those

with between 25,000 and 49,999 members, and those with 50,000 or more members. Of interest is whether the credit unions total deposits had decreased from the previous

year. The table summarizes the percentages of the three sizes of credit unions and the probability of decreasing deposits from last year to this year.
Credit union size (# members)Percentage of credit unionsProbability of
decreasing deposits
Less than 25,00091%.479
25,000 to 49,9994.7%.213
50,000 or more4.3%.117

Find the probability that a credit union selected at random had fewer than 25,000 members, given that the total deposits decreased.
The answer should show a tree diagram; the left part of the tree should have three branches (one for each of the credit union sizes). Each of these three branches

should then sprout two branches one for decreasing deposits and the other for not decreasing deposits. Each branch should be labeled with its probability. Once the

tree diagram is constructed, calculate the answer using Bayes Formula. Show the calculations, not just the answer

#2. Find the probability that a credit union selected at random had between 25,000 to 49,999 members, given that the total deposits did not decrease.
The answer should show the tree diagram and the calculations, not just the answer.

#3. The following table gives proportions of people over age 15 in the U.S. population, and proportions of people that live alone.

AgeProportion in Population

(age 15 or higher)Proportion Living Alone
15 to 24.177.038
25 to 34.169.097
35 to 44.179.086
45 to 64.318.144
65 and higher.157.287

Find the probability that a randomly selected person age 15 or older who lives alone is age 65 or older.
Show the tree diagram and the calculations, not just the answer.