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BB probability questions


Illusionz

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I'm struggling with probability problems :hmm:...can anyone recommend a good book/site for probability? It'd be deeply appreciated

Comparison Problem

 

The probability that events E and F will both occur is

0.42

 

a. The probability that event E will occur.............................b.0.58

 

-----------------------

 

30. In a group of 80 students, 24 are enrolled in

geometry, 40 in biology, and 20 in both. If a

student were randomly selected from the 80

students, what is the probability that the student

selected would not be enrolled in either course?

 

(A) 0.20

(B) 0.25

© 0.45

(D) 0.55

(E) 0.60

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2. the answer i am getting is ( C ). 0.45 .

prob( choosing a student doing neither course ) = 36 / 80 .

i m uploading an image file , a venn diagram .

 

1. at most one can say is that p( E) + p( F) = 1.42 .

bcoz , p( E or F ) = p( E) + p( F) - p( E and F ) = 1 .

=> prob( E ) >= 0.42 . also prob( F ) >= 0.42 .

so , in my view , a and b cannot be compared ( lack of info ) .

 

note even if we don't assume that E & F are exhaustive like above , what p( E and F ) = 0.42 at best gives us is that prob that E occurs is at least 0.42 , and nothing more info .

untitled.bmp

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1. P(e int f) = 0.42

 

P(e union f) = P(e) + P(f) - P(e int f)

1 = P(e) + P(f) - 0.42

P(e) + P(f) = 1.42

 

P(e) = 1.42 - P(f)

 

max pblity P(f) can have is 1 then max value of P(e) = 0.42

 

so P(e) is less than 0.52

so a

 

someone pls check

chelsea

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