Education among young adults Choose a young adult (aged 25...

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) 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?

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) 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?

Key Concepts

Mutually Exclusive Events and Partitioning

Partitioning the sample space into mutually exclusive events allows for a clear analysis where each possible outcome is considered separately without overlap. In scenarios where probabilities for distinct, non-overlapping education levels are provided, these probabilities can be added or subtracted to determine the probability of a combined event, such as aggregating the probabilities of different education categories to get the overall probability of having some education beyond high school.

Complement Rule

The Complement Rule in probability states that the probability of an event occurring is one minus the probability of that event not occurring. This rule is particularly useful when it is easier to compute the probability of the complement of an event rather than the event itself, such as finding the probability of having at least a certain level of education by subtracting the probability of not achieving that level from one.

Transcript

00:01 Okay, so for this problem, we are given this set of probabilities, and for part a, we are asked, 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? so when we're saying some education beyond high school, and we're looking at the probabilities that we're given, so we're given high school but no diploma.

00:21 We're given high school with a diploma, but no college or anything after that.

00:26 And this one is you've completed college and beyond possibly.

00:33 So the only probability missing here is the probability of having some college, but not completing a bachelor's degree.

00:41 So remembering our rules of probability, when we add up all of our probabilities, they have to equal to one.

00:48 So whenever i take my probability of some high school with no diploma, plus high school with a diploma, but nothing more.

00:57 Plus my bachelor's degree or more, plus my probability of going to college, these all need to add up to one.

01:06 Now, i have everything here that i need except for a probability of college, but i can just solve algebraically for this.

01:13 So whenever i combine like terms and subtract from both sides, my probability of going to college ends up equaling out to 0 .28.

01:23 Now, that's how we solve part a.

01:25 Now, part b asks, what is the probability? that a randomly chosen young adult has at least a high school education.

01:33 Now, if we're talking about at least a high school education, that means that they've completed high school...

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