Apparently, depression significantly increases the risk of developing dementia later in life (BBC News, July 6, 2010). In a recent study it was reported that 22% of those who had depression went on to develop dementia, compared to only 17% of those who did not have depression. Suppose 10% of all people suffer from depression.

If a person has developed dementia, what is the probability that the person suffered from depression earlier in life?(Do not round intermediate calculations. Round your answer to 3 decimal places.)

If a person has developed dementia, what is the probability that the person suffered from depression earlier in life? (Do not round intermediate calculations. Round your answer to 3 decimal places.)

0.126

Explanation:

1. Determine the percent of people who developed dementia from the entire population.

a) From the percent of people who had depression:

10% × 22% = 2.2 %

b) From the number of people who did not have depression:

90% × 17% = 15.3%

c) Total percent:

2.2% + 15.3% 17.5% of all people developed dementia.

2. Probability that the person suffered from depression earlier in life, if a person has developed dementia:

percent of people who developed dementia and had depression / percent of people who developed dementia = 2.2% / 17.5% = 0.126

Note, that this can be calculated using the formula for conditional probability:

P(A/B) = P(A∩B) / P(B)

Where:

A is having suffered depressionB is having developed dementiaA∩B is having both suffered depression and developed dementiaP(A∩B) = 22% ₓ 10% = 2.2% = 0.022P(B) = 22% × 10% + 17% × 90% = 17.5% = 0.175P(A/B) = P(A∩B) / P(B) = 0.022 / 0.175 = 0.126

500 dollars and its probably more than that

First, think of what you know. you know that the number t the end of the equation will need to be subtracted because it is the money he lost from buying the lawn mower. and your first two weeks have negative profit, so that tells you that c and d are wrong. now you can plug any of the weeks into a and b to see which one works. i'll start with plugging week 1 into a.this isn't right because it says your answer for week one should be -90.so now we need to try the same thing with b.this one got you the right answer, (sometimes if you only check with one of the weeks multiple will work so you need to check with more of the weeks, but it worked out fine here)this means that b is the correct answer.let me know if you need more clarification. i hope this : )