The following table represents the employment status and...

The following table represents the employment status and gender of the civilian labor force ages 16 to 24 (in millions). (TABLE CAN'T COPY) (a) What is the probability that a randomly selected 16 to 24-year-old individual from the civilian labor force is employed? (b) What is the probability that a randomly selected 16 to 24-year-old individual from the civilian labor force is male? (c) What is the probability that a randomly selected 16 to 24 -year-old individual from the civilian labor force is employed and male? (d) What is the probability that a randomly selected 16 to 24-year-old individual from the civilian labor force is employed or male?

The following table represents the employment status and gender of the civilian labor force ages 16 to 24 (in millions).
(TABLE CAN'T COPY)
(a) What is the probability that a randomly selected 16 to 24-year-old individual from the civilian labor force is employed?
(b) What is the probability that a randomly selected 16 to 24-year-old individual from the civilian labor force is male?
(c) What is the probability that a randomly selected 16 to 24 -year-old individual from the civilian labor force is employed and male?
(d) What is the probability that a randomly selected 16 to 24-year-old individual from the civilian labor force is employed or male?

Key Concepts

Union of Events

The union of events represents the event that at least one of the specified events occurs. The probability of a union is calculated using the addition rule, accounting for any overlap between events.

Intersection of Events

The intersection of events refers to the set containing all outcomes that satisfy both events simultaneously. Its probability quantifies the likelihood that both events occur together.

Addition Rule

The addition rule in probability states that the probability of the union of two events is equal to the sum of the probabilities of each event, minus the probability of the intersection of the two events. This rule prevents double counting the overlap between events.

Probability

Probability is a measure that quantifies the likelihood of an event occurring, defined as the ratio of the number of favorable outcomes to the total number of outcomes in a sample space.

Sample Space

The sample space is the complete set of all possible outcomes in a probability experiment. In problems like this, it represents the entire group from which a random selection is made.

Transcript

00:01 The problem we're looking at today has to do with two -way tables and finding compound probability.

00:06 So in this problem, we're given some data about the civilian workforce, ages 16 to 24, and whether they're employed or not, and whether they're male or female.

00:15 Those are the two ways, the two variables that we're looking at.

00:18 The first part of this question asks us for the probability that someone is employed.

00:24 So what we're going to focus on is this employed row, and we know 11 .2 million males and 10 .3 million females.

00:34 We need to total this up, though.

00:36 So if we total this, we know 21 .5 million are employed.

00:41 That's not the probability.

00:42 That's 21 .5 million out of the total number that they surveyed.

00:49 We don't have the total yet.

00:50 We should add that up as well.

00:52 Three million are unemployed.

00:54 So we're looking at total of 24 .5 million.

01:00 So we'll divide the variable that we want out of the total.

01:03 We'll get our percentage.

01:10 0 .877.

01:13 We'll actually round that to 8 or 87 .8%.

01:20 So there's our answer for the first one.

01:24 Now the probability that these workers are male, we'll look at the mail column.

01:30 Now again, we're going to need totals because just knowing 11 .2 and 1 .6 doesn't help us at all.

01:37 So 12 .8 is our total males, 12 .8 divided by our 24 .5 million that we had overall.

01:49 So now we'll do 12 .8 divided by 24 .5 .0 .5 to 2, 52, 52 .2 of these workers that were surveyed, these 16 to 24 -year -olds that were surveyed were male.

02:07 Now, the probability of employed and male, that's where these two overlap.

02:15 That's why i kind of left the highlighting there, because we're looking at where they overlap, which is going to put us right here with this 11 .2.

02:25 So there were 11 .2 employed male people out of our total 24 .5...

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