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Suppose that 6% of the people with blood group O are left handed and 10% of those with other blood groups are left handed 30% of the people have blood group O.If a left handed person is selected at random,what is the probability that he/she will have blood group O?

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1 Answer

Let\(E_1\) be a person selected be 'o' group
\(E_2\) be a person selected be of non 'o' group
A; He is left handed person
P(\(E_1/A\))=P(\(he\; is\; 'o' \;group/he \;is\; left \;handed\))
P(E\(_1\)/A)\(\Large\frac{{p(E_1)}{P(A/E_1)}}{{P(E_1)}{P(A/E_1)}+{P(E_2)}{P(A/E_2)}}\)
 
P\(E_1\)=P(He is 'o' group)=\(\large\frac{30}{100}\)=\(\large\frac{3}{10}\)
P\(E_2\)=P(He isnot 'o' group)=\(\large\frac{70}{100}\)=\(\large\frac{7}{10}\)
P(\(A/E_1\))=P(He is left handed /he is'O' groyp)
=\(\large\frac{6}{100}\)
P(\(A/E_2\))=P(He is left handed /he is not 'O' groyp)
=\(\large\frac{10}{100}\)
P(\(E_1/A\))=\(\Large\frac{\frac{3}{10}\times\frac{6}{100}}{\frac{3}{10}\times\frac{6}{100}+\frac{7}{10}\times\frac{10}{100}}=\frac{3\times6}{3\times6+7\times10}\)
=\(\large\frac{18}{88}\)
=\(\large\frac{9}{44}\)

 

answered Mar 1, 2013 by poojasapani_1
edited Jun 4, 2013 by poojasapani_1
 

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