Step 1: In a large national population of college students, 61% attend four-year

Question

Step 1:
In a large national population of college students, 61% attend four-year institutions and the rest attend two-year institutions. Males make up 44% of the students in the four-year institutions and 41% of the students in the two-year institutions.

Find the four probabilities for each combination of gender and type of institution in the following table. Be sure that your probabilities sum to 1.



Let = male and = attends a four-year institution.

Find the probability for a male attending a four-year institution.

Give your answer to 2 decimal places.
Fill in the blank:

= _______ .

Step 2:
In a large national population of college students, 61% attend four-year institutions and the rest attend two-year institutions. Males make up 44% of the students in the four-year institutions and 41% of the students in the two-year institutions.
Find the four probabilities for each combination of gender and type of institution in the following table. Be sure that your probabilities sum to 1.



Let = male and = attends a four-year institution.

Find the probability for a male attending a two-year institution.

Give your answer to 2 decimal places.
Fill in the blank:

   = _______ .

Step 3:
In a large national population of college students, 61% attend four-year institutions and the rest attend two-year institutions. Males make up 44% of the students in the four-year institutions and 41% of the students in the two-year institutions.
Find the four probabilities for each combination of gender and type of institution in the following table. Be sure that your probabilities sum to 1.



Let = male and = attends a four-year institution.

Find the probability for a female attending a four-year institution.

Give your answer to 2 decimal places.
Fill in the blank:

= _________.

Step 4:
In a large national population of college students, 61% attend four-year institutions and the rest attend two-year institutions. Males make up 44% of the students in the four-year institutions and 41% of the students in the two-year institutions.
Find the four probabilities for each combination of gender and type of institution in the following table. Be sure that your probabilities sum to 1.



Let = male and = attends a four-year institution.

Find the probability for a female attending a two-year institution.

Give your answer to 2 decimal places.
Fill in the blank:

= _______.

Step 5:
In a large national population of college students, 61% attend 4-year institutions and the rest attend 2-year institutions. Males make up 44% of the students in the 4-year institutions and 41% of the students in the 2-year institutions.
Find the four probabilities for each combination of gender and type of institution in the following table. Be sure that your probabilities sum to 1.



Let = male and = attends a 4-year institution.

Consider randomly selecting a female student from this population.

What is the probability that she attends a 4-year institution?
Give your answer to 2 decimal places.
Fill in the blank:

(|)= ______.

In a large national population of college students, 61% attend four-year institutions and the rest attend two-year institutions. Males make up 44% of the students in the four-year institutions and 41% of the students in the two-year institutions.
Which tree diagram illustrates the given probabilities?

Explanation / Answer

step 1.
P(C) = 0.61

male attending 4 year institution, P(M and C) = 0.44*0.61 = 0.2684

step 2.
male attending 2 year instititution
P(M and C') = 0.41*(1-0.61) = 0.1599

Step 3.
female attending 4 year institution,
P(M' and C) = 0.56*0.61 = 0.3416

step 4.
female attending 2 year institution,
P(M' and C') = 0.59*0.39 = 0.2301

step 5.
P(C|M') = P(C and M')/P(M') = 0.3416/(0.3416 + 0.2301) = 0.5975

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