Question

3) In 2004, 57% of White households directly and/or indirectly owned stocks, compared to

26% of Black households and 19% of Hispanic households. The data for Asian
households is not given, but let's assume the same rate as for Whites. Additionally, 77%
of households are classifieds as either White or Asian, 12% as African American, and
11% as Hispanic.
a) What proportion of all families owned stocks?
b) If a family owned stock, what is the probability it was White/Asian?

Answer 1

Explanation:

a) To find the proportion of all families that owned stocks, we need to calculate the weighted average of the ownership rates, where the weights are the proportions of each racial group in the total population.

Weighted average = (57% * 77%) + (26% * 12%) + (19% * 11%)

= 43.29 + 3.12 + 2.09

= 48.5%

So, 48.5% of all families owned stocks.

b) If a family owned stocks, the probability that it was White/Asian can be calculated as follows:

Probability = (Probability of being White/Asian and owning stocks) / (Probability of owning stocks)

= (57% * 77%) / (48.5%)

= (43.29) / (48.5%)

= 89.5%

Therefore, the probability that a family that owned stocks was White/Asian is 89.5%