Question

Education among young adults Chooses 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) What is the probability that a randomly chosen young adult has at least a high school education? Which rule of probability did you use to find the

answer?

Short answer

Part (a) The probability of other education is $0.28$

Part (b) The probability of completing at least high school=$0.87$

Step-by-step solution

Part (a)  Step 1. Given Information  

$P\left(A\right)=0.13$ is the probability that the person has chosen did not finish high school.$P\left(B\right)=0.29$ indicates the probability that the person has a high school diploma but no more schooling. $P\left(C\right)=0.30$indicates that the person has at least a bachelor's degree.

Part (a) Step 2. Concept Used   

An event is a subset of an experiment's total number of outcomes. The ratio of the number of elements in an event to the number of total outcomes is the probability of that occurrence.

Part (a)  Step 3. Calculation   

P(did not complete high school) = $0.13$

P(Complete high school diploma) =$0.29$

P(Bachelors degree) = $0.30$

The probability distribution requirements are as follows: $0\le p\le 1$

1)The probability should be considered $1$

2) The total of all probability should equal$1$

Using the second condition, $$\begin{gathered} 0.13+0.29+0.30+p\left(other\right)=1 \\ p\left(other\right)=1-0.72=0.28 \end{gathered}$$

Part (b) Step 1. Calculation

$P\left(A^c\right)=1-P\left(A\right)$

Using the formula of complementary probability,

$$\begin{gathered} P(atleasthighschool)=1-P(nothighschool) \\ =1-0.13 \\ =0.87 \end{gathered}$$