document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1019578>Question 1019578</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 66% of students In a class are boys and rest are girls it is known that the probability of a girl getting a first class is 0.25 and that a boy getting first class in 0.28 find the probability that a student selected at random will get first class marks in the subject </SPAN>\n" );
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document.write( "Question:<BR>\n" );
document.write( "66% of students In a class are boys and rest are girls it is known that the probability of a girl getting a first class is 0.25 and that a boy getting first class in 0.28 find the probability that a student selected at random will get first class marks in the subject<BR>\n" );
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document.write( "Solution:<BR>\n" );
document.write( "Hint: use law of total probability.<BR>\n" );
document.write( "Proportion of boys (B): 66%<BR>\n" );
document.write( "proportion of girls (G): 100-66=34%<BR>\n" );
document.write( "Let <BR>\n" );
document.write( "F=event of getting first class, then<BR>\n" );
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document.write( "P(F|B)=0.28  (probability of getting first class given that it's a boy)<BR>\n" );
document.write( "P(F|B)=P(F&cap;B)/P(B), therefore P(F&cap;B)=0.28*0.66=0.1848<BR>\n" );
document.write( " <BR>\n" );
document.write( "P(F|G)=0.25  (probability of getting first class given that it's a girl)<BR>\n" );
document.write( "P(F|G)=P(F&cap;G)/P(G), therefore P(F&cap;G)=0.25*0.34=0.085<BR>\n" );
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document.write( "Therefore probability of getting first class out of the whole class<BR>\n" );
document.write( "P(F)<BR>\n" );
document.write( "=P(F&cap;(B&cup;G))<BR>\n" );
document.write( "=P(F&cap;B)+P(F&cap;G) [since boys and girls are mutually exclusive]<BR>\n" );
document.write( "=0.1848+0.085<BR>\n" );
document.write( "=0.2698 </SPAN>\n" );
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