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 brown candy. (round all probabilities below to four decimal places; i. e. your answer should look like 0.1234, not 0.123 or 12.34%.)a.) compute the probability that the first brown candy is the seventh m& m selected. b.) compute the probability that the first brown candy is the seventh or eighth m& m selected. c.)compute the probability that the first brown candy is among the first seven m& m’s selected. d.) if every student in a large statistics class selects peanut m& m’s at random until they get a brown candy, on average how many m& m’s will the students need to select? (round your answer to two decimal places.)

See explanation.

Step-by-step explanation:

We are looking at a geometric distribution.

The probability of selecting a brown peanut is .12 = p

The probability of not selecting a brown peanut is .88 = q

The probability mass function is p(y) = (.88)^(y-1) * (.12)

a) p(7) = (.88)^6 * .12 = .0557

b) p(7 <= y <= 8) = p(7) + p(8)

   = .0557 + (.88)^7 * .12 = .1048

c) p(y <= 7) = p(0) + p(1) + ... + p(7)

   = .12 + (.88)^1 * .12 + (.88)^2 * .12 + ... + (.88)^6 * .12 = .4713

d) The expect value is 1/p. So, 1/(.12) = 8.33 M&M's

6mm^3 or .6cm^3

      216

      /   \

  36     6

  /   \     /

6     6   6

factor trees are nice.

starting with:    

5 + x - 12 = 2x - 7   

5 + x - 12 - x = 2x - 7 - x (subtract x from both sides)   

5 - 12 = x - 7 (combine and cancel x's from both sides)   

5 - 12 + 7 = x - 7 + 7 (add 7 to both sides)   

0 = x (add numbers together on both sides)       

so in order for the equation to be true, x must be 0.   

trying x = -0.5   

5 + x - 12 = 2x - 7 (original equation)   

5 + -0.5 - 12 = 2(-0.5) - 7 (plug in value of x)   

5 + -0.5 - 12 = -1 - 7 (did multiplication)   

-7.5 = -8 (did addition on both sides)       

since -7.5 is obviously not equal to -8, the value of -0.5 for x is wrong.   

trying x = 0   

5 + x - 12 = 2x - 7 (original equation)   

5 + 0 - 12 = 2(0) - 7 (plug in value of x)   

5 + 0 - 12 = 0 - 7 (did multiplication)   

-7 = -7 (did addition on both sides)       

since -7 equals -7, that demonstrates that the value of 0 for x is correct.   

trying x = 1   

5 + x - 12 = 2x - 7 (original equation)   

5 + 1 - 12 = 2(1) - 7 (plug in value of x)   

5 + 1 - 12 = 2 - 7 (did multiplication)   

-6 = -5 (did addition on both sides)       

since -6 is obviously not equal to -5, the value of 1 for x is wrong.