According to the DPT of Health Services , 12% of 30-39 have depression. Suppose 3 30-39 year olds are selected randomly what is the probability that all three will have depression.
looks like 0.12^3 to me.
A research study comparing three treatments with n = 5 in each treatment produces T1 = 5, T2 = 10, T3 = 15, with SS1 = 6, SS2 = 9, SS3 = 9, and SX2 = 94. For this study, what is SSbetween?
To calculate the probability that all three randomly selected 30-39 year olds have depression, we can use the concept of independent events. Since the individuals are selected randomly, we can assume that their depression statuses are independent of each other.
The probability that the first person has depression is given as 12%. This can be represented as 0.12 or 0.12/1.
Given that the first person has depression, the probability that the second person also has depression is still 0.12, or 0.12/1, since we are assuming independence.
Similarly, the probability that the third person has depression, given that the first two have depression, is still 0.12, or 0.12/1.
To find the probability of all three events happening, we need to multiply the individual probabilities together because, in independent events, the probabilities multiply.
So, the probability that all three randomly selected 30-39 year olds have depression is (0.12/1) * (0.12/1) * (0.12/1) = 0.001728, or approximately 0.173%.
Therefore, there is approximately a 0.173% chance that all three randomly selected 30-39 year olds will have depression, based on the given information.