document.write( "Question 1177261: 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 five peanut M&M’s from an extra-large bag of the candies. (Round all probabilities below to four decimal places; i.e. your answer should look like 0.1234, not 0.1234444 or 12.34%.)\r
\n" ); document.write( "\n" ); document.write( "Compute the probability that exactly two of the five M&M’s are orange.
\n" ); document.write( "Incorrect I set it up as 23C2 77C3
\n" ); document.write( " ---------
\n" ); document.write( " 100C5
\n" ); document.write( "Is it set up correctly?
\n" ); document.write( "Compute the probability that two or three of the five M&M’s are orange. \r
\n" ); document.write( "\n" ); document.write( "Compute the probability that at most two of the five M&M’s are orange. \r
\n" ); document.write( "\n" ); document.write( "Compute the probability that at least two of the five M&M’s are orange. $36.4714$Incorrect\r
\n" ); document.write( "\n" ); document.write( "If you repeatedly select random samples of five peanut M&M’s, on average how many do you expect to be orange? (Round your answer to two decimal places.)
\n" ); document.write( " orange M&M’s\r
\n" ); document.write( "\n" ); document.write( "With what standard deviation? (Round your answer to two decimal places.)
\n" ); document.write( " orange M&M’s \n" ); document.write( "

Algebra.Com's Answer #805635 by ikleyn(52787) $\"\"$ $\"About$

You can put this solution on YOUR website!
.
\n" ); document.write( "According to Masterfoods, the company that manufactures M&M’s, 12% of peanut M&M’s are brown,
\n" ); document.write( "15% are yellow, 12% are red, 23% are blue, 23% are orange and 15% are green.
\n" ); document.write( "You randomly select five peanut M&M’s from an extra-large bag of the candies.
\n" ); document.write( "(Round all probabilities below to four decimal places; i.e. your answer should look like 0.1234, not 0.1234444 or 12.34%.)
\n" ); document.write( "(a) Compute the probability that exactly two of the five M&M’s are orange.
\n" ); document.write( "(b) Compute the probability that two or three of the five M&M’s are orange.
\n" ); document.write( "(c) Compute the probability that at most two of the five M&M’s are orange.
\n" ); document.write( "(d) Compute the probability that at least two of the five M&M’s are orange.
\n" ); document.write( "If you repeatedly select random samples of five peanut M&M’s, on average how many do you expect to be orange? (Round your answer to two decimal places.)
\n" ); document.write( "orange M&M’s
\n" ); document.write( "With what standard deviation? (Round your answer to two decimal places.)
\n" ); document.write( "orange M&M’s
\n" ); document.write( "~~~~~~~~~~~~~~~~~\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " I will not answer all the questions - I will answer only questions (a), (b), (c) and (d).\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "

\r\n" );
document.write( "(a)  Compute the probability that exactly two of the five M&M’s are orange\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "         P(2 of 5 are red) =  =  =  = 0.2415    (rounded)      ANSWER\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "(b)  Compute the probability that two or three of the five M&M’s are orange\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "         P(2 or 3 of 5 are red) = P(2 of 5 are red) + P(3 of 5 are red) = \r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "                                =  + \r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "     I leave it to you to complete the calculations having the formula ready to use in front of you.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "(c)  Compute the probability that at most two of the five M&M’s are orange.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "         P(at most 2 of 5 are red) = P(0 of 5 are red) + P(1 of 5 are red) + P(2 of 5 are red) = \r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "                                =  +  + \r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "     I leave it to you to complete the calculations having the formula ready to use in front of you.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "(d)  Compute the probability that at least two of the five M&M’s are orange.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "         P(at least 2 of 5 are red) = P(2 of 5 are red) + P(3 of 5 are red) + P(4 of 5 are red) + P(5 of 5 are red)\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "                                =  +  +  + .\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "     I leave it to you to complete the calculations having the formula ready to use in front of you.\r\n" );
document.write( "

\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "All these questions (a) - (d) are about the BINOMIAL DOSTRIBUTION probability with the number of trials equal to 5
\n" ); document.write( "and the probability of the successful trial of 0.23.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "The number of successful trials is different in different parts from (a) to (d).\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "To see many other similar and different solved problems of this kind, look into the lessons\r
\n" ); document.write( "\n" ); document.write( "    - Simple and simplest probability problems on Binomial distribution \r
\n" ); document.write( "\n" ); document.write( "    - Typical binomial distribution probability problems \r
\n" ); document.write( "\n" ); document.write( "    - How to calculate Binomial probabilities with Technology (using MS Excel) \r
\n" ); document.write( "\n" ); document.write( "    - Solving problems on Binomial distribution with Technology (using MS Excel) \r
\n" ); document.write( "\n" ); document.write( "    - Solving problems on Binomial distribution with Technology (using online solver) \r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "in this site.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "You will find there many similar typical problems of this class, solved and explained with all details.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "After reading these lessons, you will be able to solve such problems on your own, which is your \r
\n" ); document.write( "\n" ); document.write( "PRIMARY MAJOR GOAL visiting this forum (I believe).\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

\n" );