document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1184145>Question 1184145</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The table below shows the number of mangoes and cashew of the<BR>\n" );
document.write( "same size in a bag. If two of the fruits are picked at random, one at a<BR>\n" );
document.write( "time without replacement, find the probability that:<BR>\n" );
document.write( "a. Both are good fruits b. Both are bad fruits<BR>\n" );
document.write( "c. One is a good cashew and the other bad mango.<BR>\n" );
document.write( "       Mangoes   Cashews   Total<BR>\n" );
document.write( "Good     10         6        18<BR>\n" );
document.write( "Bad      6          8        12<BR>\n" );
document.write( "Total    16        14        30 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #849875 by </B><A HREF=/tutors/aboutme.mpl?userid=CPhill><B>CPhill(1959)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=CPhill><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/cgi-bin/show-face.mpl?user=CPhill><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=849875\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Here's how to calculate the probabilities:\r<BR>\n" );
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document.write( "**a. Both are good fruits:**\r<BR>\n" );
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document.write( "* **First pick:** There are 18 good fruits out of a total of 30 fruits.  The probability of picking a good fruit first is 18/30.<BR>\n" );
document.write( "* **Second pick:** After picking one good fruit, there are now 17 good fruits left and a total of 29 fruits. The probability of picking another good fruit is 17/29.<BR>\n" );
document.write( "* **Probability of both good:**  Multiply the probabilities of each pick: (18/30) * (17/29) = 306/870 = 51/145 ≈ 0.3517\r<BR>\n" );
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document.write( "**b. Both are bad fruits:**\r<BR>\n" );
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document.write( "* **First pick:** There are 12 bad fruits out of 30 total fruits. The probability of picking a bad fruit first is 12/30.<BR>\n" );
document.write( "* **Second pick:** After picking one bad fruit, there are 11 bad fruits left and 29 total fruits. The probability of picking another bad fruit is 11/29.<BR>\n" );
document.write( "* **Probability of both bad:** Multiply the probabilities: (12/30) * (11/29) = 132/870 = 22/145 ≈ 0.1517\r<BR>\n" );
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document.write( "**c. One is a good cashew and the other a bad mango:**\r<BR>\n" );
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document.write( "There are two ways this can happen: good cashew then bad mango, or bad mango then good cashew. We have to calculate the probability of each case and then add them together.\r<BR>\n" );
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document.write( "* **Good cashew then bad mango:**<BR>\n" );
document.write( "    * Probability of good cashew first: 6/30<BR>\n" );
document.write( "    * Probability of bad mango second: 6/29<BR>\n" );
document.write( "    * Combined probability: (6/30) * (6/29) = 36/870 = 6/145 ≈ 0.0414\r<BR>\n" );
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document.write( "* **Bad mango then good cashew:**<BR>\n" );
document.write( "    * Probability of bad mango first: 6/30<BR>\n" );
document.write( "    * Probability of good cashew second: 6/29<BR>\n" );
document.write( "    * Combined probability: (6/30) * (6/29) = 36/870 = 6/145 ≈ 0.0414\r<BR>\n" );
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document.write( "* **Total probability:** Add the probabilities of the two scenarios: (6/145) + (6/145) = 12/145 ≈ 0.0828<BR>\n" );
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