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A university organization shows that 108 of the university's 253 assistant professors were women, along with 97 of the 301 associate professors and 78 of the 350 full professors. (a) What is the probability that a randomly chosen university professor (of any rank) is a woman

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MrRoyal

Answer:

[tex]Probability = 0.3131[/tex]

Step-by-step explanation:

Required

Determine the probability of selecting a woman

The given data can be represented to show women distribution as:

-------------------------------------- Women ------------------- Total

Assistant Professors ----------- 108 ----------------------253

Associate Professors ---------97 -------------------------301

Full Professors -----------------78---------------------------350

First, we calculate the number of women

[tex]Women = 108 + 97 + 78[/tex]

[tex]Women = 283[/tex]

Next, we calculate the total number of professors

[tex]Professors = 253 + 301 + 350[/tex]

[tex]Professors = 904[/tex]

Probability of selecting women is then calculated as:

[tex]Probability = \frac{Women}{Professors}[/tex]

[tex]Probability = \frac{283}{904}[/tex]

[tex]Probability = 0.31305309734[/tex]

[tex]Probability = 0.3131[/tex] -- (approximated)

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