To solve this problem, we must remember how to use PEMDAS. This tells us that we must simplify what is in parentheses first, exponents next, then multiplication and division, and finally addition and subtraction. In this case, this means that we must first perform the operations inside of the parentheses before the multiplication of the two groups of parentheses.
If we simplify within both groups of parentheses, we get:
(2+2+3+10) * (8+9+-9+7)
= (17) * (15)
We get the above simplification by performing the addition of all of the constants in the first group of parentheses and performing the addition and subtraction in the second group (notice that the +9 and -9 cancel each other out).
Now, we must simply multiply together our final two values to obtain our final answer.
For part a we define probability that the randomly selected person is if 65 years or more than that
a.
Probability of under age = 22.8% = 0.228
Probability of those from age 18 to 64 = 61.4% = 0.614
1-0.228-0.614
= 0.158
b.
P(uninsured) = p(those not up to 18) * p(those uninsured or under 18) + p(those age 18-64) * p(uninsured or under 18) + p(being 64plus) x P(uninsured or 64 plus)
= 0.228 x 0.051 + 0.614 x 0.124 + 0.158 x 0.011
= 0.011628 + 0.076136 + 0.001738
=0.089502
P(65 of older|uninsured) = p(64+) x P(uninsured or 64 plus)