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%.)
(a) Compute the probability that exactly two of the five M&M’s are orange.
(b) Compute the probability that two or three of the five M&M’s are orange.
(c) Compute the probability that at most two of the five M&M’s are orange.
(d) Compute the probability that at least two of the five M&M’s are orange. 
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.)
orange M&M’s
With what standard deviation? (Round your answer to two decimal places.)
orange M&M’s
~~~~~~~~~~~~~~~~~



            I will not answer all the questions - I will answer only questions  (a),  (b),  (c)  and  (d).



<pre>
(a)  <U>Compute the probability that exactly two of the five M&M’s are orange</U>


         P(2 of 5 are red) =  = {{{C[5]^2*0.23^2*(1-0.23)^3}}} = {{{((5*4)/(1*2))*0.23^2*0.77^3}}} = 0.2415    (rounded)      <U>ANSWER</U>




(b)  <U>Compute the probability that two or three of the five M&M’s are orange</U>


         P(2 or 3 of 5 are red) = P(2 of 5 are red) + P(3 of 5 are red) = 


                                = {{{C[5]^2*0.23^2*(1-0.23)^3}}} + {{{C[5]^3*0.23^3*(1-0.23)^2}}}


     I leave it to you to complete the calculations having the formula ready to use in front of you.




(c)  <U>Compute the probability that at most two of the five M&M’s are orange.</U>


         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) = 


                                = {{{(1-0.23)^5}}} + {{{C[5]^1*0.23^1*(1-0.23)^4}}} + {{{C[5]^2*0.23^2*(1-0.23)^3}}}


     I leave it to you to complete the calculations having the formula ready to use in front of you.




(d)  <U>Compute the probability that at least two of the five M&M’s are orange.</U>


         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)


                                = {{{C[5]^2*0.23^2*(1-0.23)^3}}} + {{{C[5]^3*0.23^3*(1-0.23)^2}}} + {{{C[5]^4*0.23^4*(1-0.23)^1}}} + {{{0.23^5}}}.


     I leave it to you to complete the calculations having the formula ready to use in front of you.
</pre>


All these questions &nbsp;(a) - (d) &nbsp;are about the &nbsp;BINOMIAL &nbsp;DOSTRIBUTION &nbsp;probability with the number of trials equal to &nbsp;5 
and the probability of the successful trial of &nbsp;0.23.


The number of successful trials is different in different parts from &nbsp;(a) &nbsp;to &nbsp;(d).



To see many other similar and different solved problems of this kind, &nbsp;look into the lessons

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/Probability-and-statistics/Solving-problems-on-Binomial-distribution-manually.lesson>Simple and simplest probability problems on Binomial distribution</A> 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/Probability-and-statistics/Typical-binomial-distribution-probability-problems.lesson>Typical binomial distribution probability problems</A> 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/Probability-and-statistics/How-to-calculate-binomial-probabilities-using-Technology.lesson>How to calculate Binomial probabilities with Technology (using MS Excel)</A> 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/Probability-and-statistics/Solving-problems-on-Binomial-distribution-using-Technology.lesson>Solving problems on Binomial distribution with Technology (using MS Excel)</A> 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/Probability-and-statistics/Solving-problems-on-Binom-distr-with-Technology-%28using-online-solver%29.lesson>Solving problems on Binomial distribution with Technology (using online solver)</A> 


in this site.


You will find there many similar typical problems of this class, &nbsp;solved and explained with all details.


After reading these lessons, &nbsp;you will be able to solve such problems on your own, which is your 

PRIMARY &nbsp;MAJOR &nbsp;GOAL &nbsp;visiting this forum &nbsp;(I believe).