Question

the accompanying table shows the numbers of male and female students in a certain region who received bachelors degrees in a certain field in a recent year. a student is selected at random. find the probability of each event listed in parts (a) through (c) below.

(a) the student is male or received a degree in the field

the probability is 0.502.
(type an integer or a decimal. round to three decimal places as needed.)

(b) the student is female or received a degree outside of the field

the probability is 0.903.
(type an integer or a decimal. round to three decimal places as needed.)

(c) the student is not female or received a degree outside of the field

the probability is .
(type an integer or a decimal. round to three decimal places as needed.)

Explanation:

Identify the given values and target event

Using the Two-Way Contingency Table Probability knowledge point
We extract the relevant frequencies from the contingency table:

• Total number of students, \(N = 1,780,374\)
• Males, \(M = 757,340\)
• Females, \(F = 1,023,034\)
• Degrees in Field, \(I = 308,725\)
• Degrees Outside of Field, \(O = 1,471,649\)
• Males with Degrees Outside of Field, \(M \cap O = 584,434\)

The target event in part (c) is: "The student is not female or received a degree outside of the field".

• "not female" is equivalent to "male" (\(M\)).
• "received a degree outside of the field" is \(O\).
• We need to find \(P(M \cup O)\).

Apply the addition rule for probability

Using the Addition Rule for Probability knowledge point

$$ P(M \cup O) = P(M) + P(O) - P(M \cap O) $$

Substituting the counts:

$$
LATEXBLOCK0
$$

Calculate the final probability

Using the Two-Way Contingency Table Probability knowledge point

$$
LATEXBLOCK1
$$

Rounding to three decimal places yields \(0.924\).

Answer:

(c) The student is not female or received a degree outside of the field

The probability is <blank>0.924</blank>
(Type an integer or a decimal. Round to three decimal places as needed.)