the probability that the girls of class 10 pass in mathematics is 6/7 and that in English is 2/7.if no girl fails in both subjects and there are 4 girls passing both,then the number of girls in the class is?

Asked by  | 7th Feb, 2014, 07:59: AM

Expert Answer:

Let the total number of girls be G.
No. of girls passing both = 4
 
Now, P(passing Maths) = P(M) = 6/7 
Then, P(M') = 1 - 6/7 = 1/7 = P(failing Maths)
 
Also, P(passing Eng) = P(E) = 2/7
Then, P(E') = 1 - 2/7 = 5/7 = P(failing Eng)
 
No. of girls failing both = 0
P(Failing in both subjects) = 0 = P left parenthesis M intersection E right parenthesis
 
No. of girls failing in only one subject = G - 4
Thus, P left parenthesis M apostrophe union E apostrophe right parenthesis equals fraction numerator G minus 4 over denominator G end fraction
Now, we have, by addition theorem,
 
P left parenthesis M apostrophe union E apostrophe right parenthesis equals P left parenthesis M apostrophe right parenthesis plus P left parenthesis E apostrophe right parenthesis minus P left parenthesis M apostrophe intersection E apostrophe right parenthesis fraction numerator G minus 4 over denominator G end fraction equals 1 over 7 plus 5 over 7 minus 0 fraction numerator G minus 4 over denominator G end fraction equals 6 over 7 7 G minus 28 space equals 6 G rightwards double arrow G equals 28

Answered by  | 7th Feb, 2014, 10:30: AM

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