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 \square.
(type an integer or a decimal. round to three decimal places as needed.)

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 \square.
(type an integer or a decimal. round to three decimal places as needed.)

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Addition Rule for Probability" ], "new_concepts": [], "current_concepts": [ "Addition Rule for Probability", "Mutually Exclusive Events", "Joint Probability Calculation" ] } ## Identify the given values and target event Using the *Addition Rule for Probability* knowledge point $$ \begin{aligned} &\text{Total number of students } (N) = 1,780,374\ &\text{Number of males } (M) = 757,340\ &\text{Number of students with degrees in the field } (F) = 308,725\ &\text{Number of males with degrees in the field } (M \cap F) = 172,906 \end{aligned} $$ ## Apply the addition rule formula Using the *Addition Rule for Probability* knowledge point $$ \begin{aligned} P(M \cup F) &= P(M) + P(F) - P(M \cap F)\ &= \frac{757,340}{1,780,374} + \frac{308,725}{1,780,374} - \frac{172,906}{1,780,374}\ &= \frac{757,340 + 308,725 - 172,906}{1,780,374} \end{aligned} $$ ## Calculate the final probability Using the *Addition Rule for Probability* knowledge point $$ \begin{aligned} \text{Numerator} &= 893,159\ P(M \cup F) &= \frac{893,159}{1,780,374} \approx 0.50167\ &\approx 0.502 \end{aligned} $$ (a) The student is male or received a degree in the field The probability is 0.502. { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Statistics", "Addition Rule for Probability" ] }

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Question

Explanation:

Identify the given values and target event

Apply the addition rule formula

Calculate the final probability

Answer: