Question

in 1970, 85% of 30 - year - olds in a country earned more than their parents did at age 30 (adjusted for inflation). in 2014, only 45% of 30 - year - olds in the same country earned more than their parents did at age 30. complete parts a to d below.
(a) what is the probability a randomly selected 30 - year - old in 1970 earned more than their parents at age 30?
the probability is 0.8500.
(round to four decimal places as needed.)
(b) what is the probability that two randomly selected 30 - year - olds in 1970 earned more than their parents at age 30?
the probability is
(round to four decimal places as needed.)

Explanation:

Step1: Identify probability of single - event

The probability that a single 30 - year - old in 1970 earned more than their parents at age 30 is $p = 0.85$.

Step2: Use multiplication rule for independent events

Since the events of two randomly selected 30 - year - olds earning more than their parents are independent, the probability that two such 30 - year - olds both earned more than their parents is $p\times p$.
$0.85\times0.85= 0.7225$

Answer:

$0.7225$