(a) The student is male or recelved a degree in the field The probability is 0.519 . (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 \( 0.905^{3} \). (Type an integer or a decimal. Round to three decimal places as needed) (c) The student is not fermale or received a degree outside of the field The probability is (Iype an integer or a decimal. Round to three decimal places as needed)

Let's denote the following events: - \( A \): The student is male - \( B \): The student received a degree in the field Given probabilities: - \( P(A \cup B) = 0.519 \) - \( P(\text{Female} \cup \text{Degree outside of the field}) = 0.905^3 \) We need to find the probability of the following events: (a) The student is male or received a degree in the field (b) The student is female or received a degree outside of the field (c) The student is not female or received a degree outside of the field Let's calculate these probabilities step by step: (a) The probability of the student being male or received a degree in the field: \[ P(A \cup B) = P(A) + P(B) - P(A \cap B) \] Given that \( P(A \cup B) = 0.519 \), we need to find \( P(A) \) and \( P(B) \) to calculate this probability. (b) The probability of the student being female or received a degree outside of the field: \[ P(\text{Female} \cup \text{Degree outside of the field}) = P(\text{Female}) + P(\text{Degree outside of the field}) - P(\text{Female} \cap \text{Degree outside of the field}) \] Given that \( P(\text{Female} \cup \text{Degree outside of the field}) = 0.905^3 \), we need to find \( P(\text{Female}) \) and \( P(\text{Degree outside of the field}) \) to calculate this probability. (c) The probability of the student being not female or received a degree outside of the field: \[ P(\text{Not Female} \cup \text{Degree outside of the field}) = P(\text{Not Female}) + P(\text{Degree outside of the field}) - P(\text{Not Female} \cap \text{Degree outside of the field}) \] Given that \( P(\text{Not Female} \cup \text{Degree outside of the field}) \), we need to find \( P(\text{Not Female}) \) and \( P(\text{Degree outside of the field}) \) to calculate this probability. Let's calculate these probabilities step by step. Numbers by following steps: - step0: Solution: \(0.519\) The probability of the student being male or received a degree in the field is \(0.519\) or \(\frac{519}{1000}\). Next, let's calculate the probability of the student being female or received a degree outside of the field. Calculate the value by following steps: - step0: Calculate: \(0.905^{3}\) - step1: Convert the expressions: \(\left(\frac{181}{200}\right)^{3}\) - step2: Use the properties of exponents: \(\frac{181^{3}}{200^{3}}\) The probability of the student being female or received a degree outside of the field is \(0.741217625\) or \(\frac{181^{3}}{200^{3}}\). Finally, let's calculate the probability of the student being not female or received a degree outside of the field. Calculate the value by following steps: - step0: Calculate: \(1-0.905^{3}\) - step1: Convert the expressions: \(1-\left(\frac{181}{200}\right)^{3}\) - step2: Rewrite the expression: \(1-\frac{181^{3}}{200^{3}}\) - step3: Reduce fractions to a common denominator: \(\frac{200^{3}}{200^{3}}-\frac{181^{3}}{200^{3}}\) - step4: Transform the expression: \(\frac{200^{3}-181^{3}}{200^{3}}\) The probability of the student being not female or received a degree outside of the field is \(0.258782375\) or \(\frac{200^{3}-181^{3}}{200^{3}}\). Therefore, the probabilities are: (a) The probability of the student being male or received a degree in the field is \(0.519\) or \(\frac{519}{1000}\). (b) The probability of the student being female or received a degree outside of the field is \(0.741217625\) or \(\frac{181^{3}}{200^{3}}\). (c) The probability of the student being not female or received a degree outside of the field is \(0.258782375\) or \(\frac{200^{3}-181^{3}}{200^{3}}\).