document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1118158>Question 1118158</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A bag contains 10 red, 8 green and 7 blue balls, If two balls are picked at random one after the other without replacement from the bag, what is the probability that: <BR>\n" );
document.write( "(i) they are of the different colors<BR>\n" );
document.write( "(ii) at least a ball is blue? </SPAN>\n" );
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document.write( "There are many ways to calculate probabilities like these.<br><BR>\n" );
document.write( "Basically, you want to put the worded requirements in terms of ANDs and/or ORs and then, in your calculations, replace each AND with a multiplication and each OR with an addition.<br><BR>\n" );
document.write( "You can count the number of ways of getting the desired outcome and get the probability by dividing by the total number of ways of choosing 2 of the 25 balls, which is C(25,2) = 300.<br><BR>\n" );
document.write( "Or you can think of drawing one ball at a time and work with the probability of good outcomes on each draw.<br><BR>\n" );
document.write( "Following are a few ways you could do the second problem.<br><BR>\n" );
document.write( "(1) Find the number of ways of choosing 2 of the 7 blue balls AND none of the 18 other colors OR 1 of the 7 blue balls AND 1 of the other 18 balls:<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C%287%2C2%29%2AC%2818%2C0%29%2BC%287%2C1%29%2AC%2818%2C1%29+=+21%2A1%2B7%2A18+=+21%2B126+=+147 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Then the probability is 147/300.<br><BR>\n" );
document.write( "(2) Find the probability of choosing a blue ball AND then another blue ball, OR choosing a blue ball AND then a different color ball, OR choosing a different color ball and then a blue ball:<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%287%2F25%29%2A%286%2F24%29%2B%287%2F25%29%2A%2818%2F24%29%2B%2818%2F25%29%2A%287%2F24%29+=+%2842%2B126%2B126%29%2F600+=+294%2F600+=+147%2F300. ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "(3) Find the number of ways of choosing 2 balls which are both NOT blue; convert that number to a probability, and subtract from 1:<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C%2818%2C2%29+=+153 ALIGN=MIDDLE  ALT=\"C%2818%2C2%29+=+153\"   DISABLED_style= \"max-width:90%; height:auto;\" >; <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1-153%2F300+=+147%2F300 ALIGN=MIDDLE  ALT=\"1-153%2F300+=+147%2F300\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "(4) Find the probability of choosing a ball that is not blue AND then another ball that is not blue, and subtract that from 1:<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1+-+%2818%2F25%29%2A%2817%2F24%29+=+1+-+306%2F600+=+1-153%2F300+=+147%2F300 ALIGN=MIDDLE  ALT=\"1+-+%2818%2F25%29%2A%2817%2F24%29+=+1+-+306%2F600+=+1-153%2F300+=+147%2F300\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "I would strongly recommend that you try solving problems like this in at least a couple of different ways.  Seeing that you can use different methods to get the same right answer gives you confidence in the work you are doing.<br><BR>\n" );
document.write( "I will just note a couple of ways you can work the first problem, using methods similar to those above.<br><BR>\n" );
document.write( "(1) Find the number of ways of choosing 1 red AND 1 blue OR 1 red AND 1 green OR 1 blue AND 1 green; add and convert to a probability by dividing by 300.<br><BR>\n" );
document.write( "(2) Find the number of ways of getting 1 red AND 1 of either other color OR of getting 1 blue AND 1 green; convert to a probability as in the other method.<br><BR>\n" );
document.write( "(3) Find the probability of getting a blue AND then a different color, OR getting a red AND then a different color, OR getting a green AND then a different color.<br><BR>\n" );
document.write( "(4) Find the probability of getting 2 blue OR 2 red OR 2 green and subtract from 1. </SPAN>\n" );
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