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October 18th, 2009, 07:56 PM   #1
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Help with a probability problem

OK, I can't seem to figure this out logically... any help?

61% of students attend 4-year institutions and 39% 2-year institutions.
4-Year Institutions 2-Year Institutions
Males: 44% Males: 41%
Females: 56% Females: 59%

a) Find the four probabilities of each combo of gender and type of institution in a table. Be sure that probabilities sum to 1.

Men Women
4-Year Institution 0.44 0.56
2-Year Institution 0.41 0.59

b) Consider randomly selecting a female student from this population. What is the probability that she attends a 4-Year Institution?


P (Four-year and two-year) = P (
P (Four-year)
0.56 + 0.59 - .44 - .41 =

(Is this a conditional probability? If not, what is it?)
al_teothc is offline  
 
October 19th, 2009, 03:48 PM   #2
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Re: Help with a probability problem

a) the four probabilities of each combo of gender and type of institution
P(Male and attends 4 year institution) = 0.61 * 0.44 = 0.2684
P(Female and attends 4 year institution) = 0.61 * 0.56 = 0.3416
P(Male and attends 2 year institution) = 0.39 * 0.41 = 0.1599
P(Female and attends 2 year institution) = 0.39 * 0.59 = 0.2301

You can now put these probabilities into a table. (These probabilities sum to 1)

b) Yes. This one s a conditional probability

P(attends 4 year institution | female)

= P(attends 4 year instition and female) / P(female)

= 0.3416 /(0.3416 + 0.2301)

= 0.5975

Cheers
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