document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1199667>Question 1199667</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Jon buys a bag of cookies that contains 7 chocolate chip cookies, 6 peanut butter cookies, 8 sugar cookies and 5 oatmeal cookies. What is the probability that Jon randomly selects a chocolate chip cookie from the bag, eats it, then randomly selects a sugar cookie?\r<BR>\n" );
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document.write( "Probability = <BR>\n" );
document.write( "   (Round to 4 decimal places) </SPAN>\n" );
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document.write( "A = event of selecting a chocolate chip cookie on the 1st selection<BR>\n" );
document.write( "P(A) = (number of chocolate chip)/(number total)<BR>\n" );
document.write( "P(A) = (7 chocolate chip)/(7+6+8+5 total)<BR>\n" );
document.write( "P(A) = (7 chocolate chip)/(26 total)<BR>\n" );
document.write( "P(A) = 7/26\r<BR>\n" );
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document.write( "The fact that Jon eats the 1st cookie means no replacement is done.<BR>\n" );
document.write( "This will affect the probability of the 2nd cookie (hence the events aren't independent).\r<BR>\n" );
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document.write( "B = event of selecting a sugar cookie on the 2nd selection\r<BR>\n" );
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document.write( "P(B given A) = probability B happens if event A happened<BR>\n" );
document.write( "P(B given A) = (number of sugar cookies)/(total number left)<BR>\n" );
document.write( "P(B given A) = (8 sugar cookies)/(26-1 left over)<BR>\n" );
document.write( "P(B given A) = (8 sugar cookies)/(25 left over)<BR>\n" );
document.write( "P(B given A) = 8/25<BR>\n" );
document.write( "For more information, search out \"conditional probability\".\r<BR>\n" );
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document.write( "Lastly,<BR>\n" );
document.write( "P(A and B) = P(A) * P(B given A)<BR>\n" );
document.write( "P(A and B) = (7/26)*(8/25)<BR>\n" );
document.write( "P(A and B) = 0.08615384615384 approximately<BR>\n" );
document.write( "P(A and B) = 0.0862<BR>\n" );
document.write( "There's about an 8.62% chance of this happening.\r<BR>\n" );
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document.write( "-----------------------------------------------------\r<BR>\n" );
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document.write( "Answer: <font color=red size=4>0.0862</font><BR>\n" );
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