The table shows the numbers (in thousands) of earned degrees by level in two different fields, conferred in the United States in a recent year. (Source: U.S. National Center for Education Statistics)
A person who earned a degree in the year is randomly selected. Find the probability that the degree earned by the person is a
g. bachelor's degree and the degree is in natural sciences/mathematics.

Verified step by step guidance

Step 1: Identify the relevant data from the table. The number of bachelor's degrees in natural sciences/mathematics is 175.5 (in thousands), and the total number of degrees conferred across all fields and levels is 565.4 (in thousands).

Step 2: Recall the formula for probability. The probability of an event is calculated as the ratio of the number of favorable outcomes to the total number of outcomes. In this case, the favorable outcome is earning a bachelor's degree in natural sciences/mathematics.

Step 3: Write the probability formula for this scenario: \( P = \frac{\text{Number of bachelor's degrees in natural sciences/mathematics}}{\text{Total number of degrees}} \). Using MathML, this can be expressed as:

P = \frac{175.5}{565.4}

Step 4: Simplify the fraction to calculate the probability. This involves dividing the numerator (175.5) by the denominator (565.4).

Step 5: Interpret the result. The probability represents the likelihood that a randomly selected person who earned a degree in the year earned a bachelor's degree in natural sciences/mathematics.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Probability

Probability is a measure of the likelihood that a particular event will occur, expressed as a number between 0 and 1. In this context, it involves calculating the chance that a randomly selected degree is a bachelor's degree in natural sciences/mathematics. This is determined by dividing the number of bachelor's degrees in that field by the total number of degrees conferred.

Conditional Probability

Conditional probability refers to the probability of an event occurring given that another event has already occurred. In this scenario, it helps in understanding how the selection of a degree type (bachelor's) influences the probability of it being in a specific field (natural sciences/mathematics). This concept is crucial for interpreting the results accurately.

Data Interpretation

Data interpretation involves analyzing and making sense of data presented in tables or graphs. In this case, it requires extracting relevant figures from the provided table to compute the desired probability. Understanding how to read and interpret the data accurately is essential for solving the problem effectively.

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