document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=519264>Question 519264</A>: <I><SPAN STYLE=\"word-break: break-all;\"> please help.<BR>\n" );
document.write( "A box contains 20 chocolates, of which fifteen have soft centres and five hard centres. Two chocolates are taken at random, one after the other. Calculate the probability that<BR>\n" );
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document.write( "  i. both chocolates have soft centres\r<BR>\n" );
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document.write( " ii. One of each sort of chocolate is taken\r<BR>\n" );
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document.write( " iii. Both types (soft and hard), given that the second chocolate has a hard centre.\r<BR>\n" );
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document.write( "Thank you. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #345481 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=345481\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A box contains 20 chocolates, of which fifteen have soft centres and five hard centres. Two chocolates are taken at random, one after the other. Calculate the probability that\r<BR>\n" );
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document.write( "i. both chocolates have soft centres<BR>\n" );
document.write( "P(soft AND soft) = P(soft)*P(soft|soft) = (15/20)(14/19)=0.5526 <BR>\n" );
document.write( "ii. One of each sort of chocolate is taken<BR>\n" );
document.write( "Since P(hard AND hard) = (5/20)(4/19) = 0.0526<BR>\n" );
document.write( "P(one of each) = 1-[P(2 soft)+P(2 hard)] = 1-[0.5526+0.0526] = 0.3948<BR>\n" );
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document.write( "iii. Both types (soft and hard), given that the second chocolate has a hard centre. <BR>\n" );
document.write( "P(hard|soft) = P(hard and soft)/P(soft) = 0.3948/(15/20) = 0.5264<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
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