Math Is Fun Forum

qweiop90

Member

Registered: 2008-08-19

Posts: 8

probability =(

the probability a girl who wears spectacles is 1/12 and the probability a student who wears spectacles is a girl is 1/9. the probability that a student selected randomly is not a girl and does not wear spectacles is 3/4. wht is the probability that a person chosen randomly is a girl who wear spectacles? answer provided1/80

2)among 10 000 candidATES who are applying to be admitted to teaching college, only 2200 are selected to sit for the written test. For evry 100 candidates who sit for the written test, 70 will be called for an oral interview. For every 10 candidates interviewed, 3 will successfully join the Teaching colleges.

a) what is the probability that an applicant will reach the stage of the interview?(0.154)
b) What is the probability that an applicant who is sitting for the written test suceeds in entering a Teaching College?(0.21)
c) What is the probability an applicant will succeed in entering a teaching college?(0.0462)

3)A dice is tossed 4 times. find the probability that we will obtain the number 4 exactly .(25/256*)

Last edited by qweiop90 (2008-08-20 15:22:32)

John E. Franklin

Member

Registered: 2005-08-29

Posts: 3,588

Re: probability =(

"tmz" means multiply.
2a.) .22 tmz .7    2b.) .7 tmz .3   2c.)  .22 tmz .7 tmz .3

prob 1 & 3 still left to do...

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igloo myrtilles fourmis

qweiop90

Member

Registered: 2008-08-19

Posts: 8

Re: probability =(

dont get wht u mean -.-

John E. Franklin

Member

Registered: 2005-08-29

Posts: 3,588

Re: probability =(

"cut" means "divided by".
2200 cut 10000 is .22
70 cut 100 is .7
3 cut 10 is .3

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igloo myrtilles fourmis

qweiop90

Member

Registered: 2008-08-19

Posts: 8

Re: probability =(

ok understood . i dont understand question 1) , for question3 , it should be 1/6 X 5/6 X 5/6 . i would like to ask if the number repeated is twice, so we consider 1 of the probability?

gnitsuk

Member

Registered: 2006-02-09

Posts: 121

Re: probability =(

Here's the answer to question (1):

We need to use the conditional probability formula:

(trivially provable  - http://www.stat.yale.edu/Courses/1997-9 … ndprob.htm)

Also obvious is that:

So lets go:

Let

P(S|G) = Probability that a person wears spectacles given that they are a girl
P(G|S) = Probability that a person  is a girl given that they wear spectacles
P(C) = Probability that a person picked at random is neither a girl nor wears spectacles

We are given:

It is plainly clear from a Venn diagram that:

Call this "Forumula A"

So lets keep our terminology simple and define:

D = P(G)
E = P(S)
F = P(GnS)

Note that it is F that we are asked to find.

Now here's where we use the conditional probability formulae:

So from Formula A we have:

Remember we know the numerical values of A and B, so let's put them in:

Solve this for F to get the desired:

(Further reading - http://en.wikipedia.org/wiki/Bayes%27_theorem)

Last edited by gnitsuk (2008-08-21 22:53:27)