The table below represents the college degrees awarded in a...

The table below represents the college degrees awarded in a recent academic year by gender. $$ \begin{array}{lccc} & \text { Bachelor's } & \text { Master's } & \text { Doctorate } \\ \hline \text { Men } & 573,079 & 211,381 & 24,341 \\ \text { Women } & 775,424 & 301,264 & 21,683 \end{array} $$ Choose a degree at random. Find the probability that it is a. A bachelor's degree b. A doctorate or a degree awarded to a woman c. A doctorate awarded to a woman d. Not a master's degree

The table below represents the college degrees awarded in a recent academic year by gender.
$$
\begin{array}{lccc}
& \text { Bachelor's } & \text { Master's } & \text { Doctorate } \\
\hline \text { Men } & 573,079 & 211,381 & 24,341 \\
\text { Women } & 775,424 & 301,264 & 21,683
\end{array}
$$
Choose a degree at random. Find the probability that it is
a. A bachelor's degree
b. A doctorate or a degree awarded to a woman
c. A doctorate awarded to a woman
d. Not a master's degree

Key Concepts

Probability

Probability is a measure of how likely an event is to occur, defined as the ratio of the number of favorable outcomes to the total number of possible outcomes. In problems like this, probabilities are calculated by dividing the count of degrees that meet a certain criterion by the overall count of degrees awarded.

Sample Space

The sample space in probability theory is the set of all possible outcomes. In this context, the sample space consists of every degree awarded, with each degree being a unit in the total sum. Calculating probabilities involves finding the total number of outcomes in the sample space.

Counting Techniques

Counting techniques involve summing or aggregating groups of outcomes to determine the total number of favorable results or total outcomes. When data is organized in a table or categorized format, these techniques are used to add up the counts from different categories to analyze probabilities.

Union of Events

The union of two events refers to the situation where at least one of the events occurs. In probability problems, the probability of the union of events is calculated by adding their individual probabilities and then subtracting any overlap, ensuring that outcomes common to both events aren’t counted twice.

Intersection of Events

The intersection of events refers to outcomes that satisfy two conditions simultaneously. For instance, finding the probability of one outcome that meets two criteria involves identifying the overlap between the events and calculating the probability based on the count of outcomes in this intersection relative to the total number in the sample space.

Complement of an Event

The complement of an event includes all outcomes that do not satisfy the event's conditions. In probability, finding the probability of the complement is often simpler by subtracting the probability of the event from one, especially when it’s easier to calculate the occurrence of the event than its absence.

Transcript

00:01 Okay, so i see that you need help with this question and so we have men woman and we need to find the totals.

00:13 We have a bachelor's degree master's degree and doctoral degree and then we need our total.

00:23 Okay, so bachelors is 57309079 and then seven seven five four two four then two one one three eight one then three zero one two six four then we have two four three four one then we have two one six eight three, so it is five seven three five seven three zero seven nine plus seven seven five four two four that's one three four eight five zero three two one one three eight one plus three zero one two six four that's five one two six four five then two four three three four one plus two one six eight three and that's two six five zero two four then i have plus five one two six four five plus one three four eight five zero three that's two one two six one seven two then i have seven seven five four two four plus three zero one two six four plus two one six eight three that is one zero nine eight three seven one then i have five seven three zero seven nine plus two one one three eight one plus two four three four one.

02:17 That's eight zero eight eight zero one, okay, so first question it asks the following let me just get rid of these lines right here okay, choose a degree at random find the probability that it is a a bachelor's degree so that's one three four eight five zero three out of two one two six one seven two so one three oops one three four eight five zero three divided by two one two six one seven two and that's equal to zero point six three four two three four two three nine eight four five i'm not sure what they want you to round to then be a doctorate or a degree awarded to a woman so that's a doctorate or a degree awarded to the woman.

03:34 So that would be one zero nine eight three seven one plus two six five zero two four minus two one six eight three because i don't want to add it in twice out of two one two six one seven two so that is going to be one zero nine eight three seven one plus two six five zero two four minus two one six eight three so that's one three four one seven one two divided by two one two six one seven two divided by two one two six one seven two and that is zero point six three one then see a doctorate awarded to a woman so a doctorate awarded to a woman...

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