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Use the Rule of Total Probability to Find the Indicated

question 21

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Use the rule of total probability to find the indicated probability.
-Among students at one college are 3874 women and 3058 men. The following table provides relative-frequency distributions for subject major for males and females at the college.  Major  Relative frequency  for women  Relative frequency  for men  Humanities 0.1870.165 Science 0.2840.349 Social Science 0.1420.179 Other 0.3870.307\begin{array} { l c c } \text { Major } & \begin{array} { l } \text { Relative frequency } \\\text { for women }\end{array} & \begin{array} { l } \text { Relative frequency } \\\text { for men }\end{array} \\\hline \text { Humanities } & 0.187 & 0.165 \\\text { Science } & 0.284 & 0.349 \\\text { Social Science } & 0.142 & 0.179 \\\text { Other } & 0.387 & 0.307\end{array} A student is selected at random from the college. Determine the probability that the student is a Science major.

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Definitions:

Pulmonary Arteries

The arteries that carry deoxygenated blood from the heart to the lungs, where it is oxygenated before being returned to the heart.

Lungs

Organs in the respiratory system involved in the exchange of oxygen and carbon dioxide between the body and the environment.

Cerebral Arterial Circle

Also known as the Circle of Willis, this is a circulatory anastomosis that supplies blood to the brain and surrounding structures.

Posterior Cerebellar Artery

A branch of the vertebral artery that supplies blood to the cerebellum, crucial for balance and smooth movements.

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