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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鈥檚 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鈥檚 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 $0.58$ .