Education among young adults Choose a young adult (aged $25$to $29$) at random. The probability is $0.13$that the person chosen did not complete high school, $0.29$that the person has a high school diploma but no further education, and $0.30$that the person has at least a bachelor’s degree.

a. What must be the probability that a randomly chosen young adult has some education beyond high school but does not have a bachelor’s degree? Why?

b. Find the probability that the young adult completed high school. Which probability rule did you use to find the answer?

c. Find the probability that the young adult has further education beyond high school. Which probability rule did you use to find the answer?

We need to find what must be the probability that a randomly chosen young adult has some education beyond high school but does not have a bachelor’s degree.

Persons who did not finish high school have a probability of $0.13$.
Probability of someone who graduated from high school but did not pursue additional education = $0.29$
Person with at least a bachelor's degree has a $0.30$ probability.
Calculation:

Because the total of the probabilities is $1$,

The probability of someone with some post-secondary education but no bachelor's degree is
$=1-0.13-0.29-0.30=0.28$
Hence, $0.28$ must be the probability that a randomly chosen young adult has some education beyond high school but does not have a bachelor’s degree.

We need to find the probability that the young adult completed high school.

As we know by concept of addition rule of mutually exclusive cases,

P(high school) is sum of P(completed high school diploma but no further education) and P(at least bachelor's degree) and P(completed high school diploma but no bachelor's degree)

P(completed high school diploma but no further education) : $0.29$

P(at least bachelor's degree) : $0.30$

P(completed high school diploma but no bachelor's degree) : $0.28$

Therefore,

P(high school) : $0.29+0.30+0.28=0.87$

Hence, The probability that the young adult completed high school is $0.87$.

We need to find the probability that the young adult has further education beyond high school.

As we know by concept of addition rule of mutually exclusive cases,

P (further education beyond high school) is sum of P( at least bachelor's degree) and P(completed high school but doesn't have bachelor's degree)

P( at least bachelor's degree) : $0.30$

P(completed high school but doesn't have bachelor's degree) : $0.28$

Therefore,

P (further education beyond high school) : $0.30+0.28=0.58$

Hence, The probability that the young adult has further education beyond high school is $0.58$ .