document.write( "Question 1191331: According to Masterfoods, the company that manufactures M&M’s, 12% of peanut M&M’s are brown, 15% are yellow, 12% are red, 23% are blue, 23% are orange and 15% are green. You randomly select peanut M&M’s from an extra-large bag looking for a yellow candy. (Round all probabilities below to four decimal places; i.e. your answer should look like 0.1234, not 12.34%.)\r
\n" ); document.write( "\n" ); document.write( "a) Compute the probability that the first yellow candy is the sixth M&M selected.\r
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\n" ); document.write( "\n" ); document.write( "b) Compute the probability that the first yellow candy is the sixth or seventh M&M selected.\r
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\n" ); document.write( "\n" ); document.write( "c) Compute the probability that the first yellow candy is among the first six M&M’s selected.\r
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\n" ); document.write( "\n" ); document.write( "d) If every student in a large Statistics class selects peanut M&M’s at random until they get a yellow candy, on average how many M&M’s will the students need to select? (Round your answer to two decimal places.)\r
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Algebra.Com's Answer #823149 by ikleyn(52781) $\"\"$ $\"About$

You can put this solution on YOUR website!
According to Masterfoods, the company that manufactures M&M’s, 12% of peanut M&M’s are brown, 15% are yellow,
\n" ); document.write( "12% are red, 23% are blue, 23% are orange and 15% are green.
\n" ); document.write( "You randomly select peanut M&M’s from an extra-large bag looking for a yellow candy.
\n" ); document.write( "(Round all probabilities below to four decimal places; i.e. your answer should look like 0.1234, not 12.34%.)\r
\n" ); document.write( "\n" ); document.write( "a) Compute the probability that the first yellow candy is the sixth M&M selected.\r
\n" ); document.write( "\n" ); document.write( "b) Compute the probability that the first yellow candy is the sixth or seventh M&M selected.\r
\n" ); document.write( "\n" ); document.write( "c) Compute the probability that the first yellow candy is among the first six M&M’s selected.\r
\n" ); document.write( "\n" ); document.write( "d) If every student in a large Statistics class selects peanut M&M’s at random until they get a yellow candy,
\n" ); document.write( "on average how many M&M’s will the students need to select? (Round your answer to two decimal places.)
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\n" ); document.write( "\n" ); document.write( "Tooooooo many questions to answer all of them at a time.\r
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\n" ); document.write( "\n" ); document.write( "In this post, I will answer (a), (b) and (c), only.\r
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\n" ); document.write( "\n" ); document.write( "The major idea is to recognize that we have a Binomial distribution probability problem with the success
\n" ); document.write( "individual trial probability of 0.15 for yellow and (1-0.15) = 0.85 for not yellow.\r
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document.write( "(a)  P(the first yellow candy is the sixth M&M selected) = 0.85^5*0.15 = 0.06656   (rounded).\r\n" );
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document.write( "(b)  P(the first yellow candy is the sixth or seventh M&M selected) = 0.85^5*0.15 + 0.85^6*0.15 = 0.1231     (rounded).\r\n" );
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document.write( "(c)  P(the first yellow candy is among the first six M&M’s selected) = \r\n" );
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document.write( "         = is the same as (simply re-phrasing) =  \r\n" );
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document.write( "  =  P(exactly one yellow is among the first six M&M’s selected) = \r\n" );
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document.write( "  =   =  = 0.3993.\r\n" );
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