document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1195096>Question 1195096</A>: <I><SPAN STYLE=\"word-break: break-all;\"> You are sent to the local tea shop to pick up 15 drinks. You purchase 8 sweet teas and 7 unsweetened teas. Unfortunately, you forgot to label them. If you pick 3 drinks at random, find the probability of each event below. Give your answers as simplified fractions.\r<BR>\n" );
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document.write( "a) All of the 3 drinks picked are sweet teas.<BR>\n" );
document.write( "b) Exactly one drink is sweetened. </SPAN>\n" );
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document.write( "Part (a)\r<BR>\n" );
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document.write( "8/15 is the probability of getting a sweet tea if chosen at random. This is simply because there are 8 sweet teas out of 15 drinks total.\r<BR>\n" );
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document.write( "7/14 is the probability of getting another sweet tea. <BR>\n" );
document.write( "Subtract 1 from both the top and bottom of 8/15 to get 7/14. <BR>\n" );
document.write( "I recommend not reducing because while 7/14 = 1/2 is easier to deal with, it makes it tricky to connect back to 8/15 again.\r<BR>\n" );
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document.write( "6/13 is the probability of getting a third sweet tea. \r<BR>\n" );
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document.write( "The probabilities are:<BR>\n" );
document.write( "8/15 for the first sweet drink<BR>\n" );
document.write( "7/14 for the second sweet drink<BR>\n" );
document.write( "6/13 for the third sweet drink\r<BR>\n" );
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document.write( "The numerators count down: 8, 7, 6<BR>\n" );
document.write( "So do the denominators: 15, 14, 13\r<BR>\n" );
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document.write( "Multiply those fractions to get the answer. <BR>\n" );
document.write( "At this point, we will reduce the result as much as possible.<BR>\n" );
document.write( "(8/15)*(7/14)*(6/13)<BR>\n" );
document.write( "(8*7*6)/(15*14*13)<BR>\n" );
document.write( "336/2730<BR>\n" );
document.write( "(8*42)/(65*42)<BR>\n" );
document.write( "8/65\r<BR>\n" );
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document.write( "Answer: <font color=red>8/65</font>\r<BR>\n" );
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document.write( "Part (b)\r<BR>\n" );
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document.write( "8/15 is the probability of getting a sweet tea. Refer to part (a) earlier.\r<BR>\n" );
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document.write( "After that sweet tea is chosen, we have 7 unsweetened teas out of 15-1 = 14 left over. <BR>\n" );
document.write( "Coincidentally we get 7/14 once again. <BR>\n" );
document.write( "This also leads to 6/13 as the probability of getting another unsweetened tea in the third selection.\r<BR>\n" );
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document.write( "We have these probabilities:<BR>\n" );
document.write( "8/15 = first selection is sweet<BR>\n" );
document.write( "7/14 = second selection is unsweetened<BR>\n" );
document.write( "6/13 = third selection is unsweetened\r<BR>\n" );
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document.write( "(8/15)*(7/14)*(6/13) = 8/65 is the probability of getting the above items in the order mentioned.\r<BR>\n" );
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document.write( "We triple this result because we could get a sweet tea in any of the three slots<BR>\n" );
document.write( "3*(8/65) = 24/65\r<BR>\n" );
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document.write( "Answer: <font color=red>24/65</font><BR>\n" );
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