1.) According to Masterfoods, the company that manufactures M&M’s, 12% of peanut
ID: 3069667 • Letter: 1
Question
1.) 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. (Round your answers to 4 decimal places where possible)
a. Compute the probability that a randomly selected peanut M&M is not blue.
b. Compute the probability that a randomly selected peanut M&M is green or orange.
c. Compute the probability that three randomly selected peanut M&M’s are all yellow.
d. If you randomly select three peanut M&M’s, compute that probability that none of them are blue.
e. If you randomly select three peanut M&M’s, compute that probability that at least one of them is blue.
2.)
At a drug rehab center 35% experience depression and 31% experience weight gain. 17% experience both. If a patient from the center is randomly selected, find the probability that the patient (Round all answers to four decimal places where possible.)
a. experiences neither depression nor weight gain.
b. experiences depression given that the patient experiences weight gain.
c. experiences weight gain given that the patient experiences depression. (round to 4 decimal places)
d. Are depression and weight gain mutually exclusive?
yes
no
e. Are depression and weight gain independent?
yes
no
3.)
A 2010 Pew Research poll asked 1,306 Americans "From what you've read and heard, is there solid evidence that the average temperature on earth has been getting warmer over the past few decades, or not?". The table below shows the distribution of responses by party and ideology, where the counts have been replaced with relative frequencies.
a) Are believing that the earth is warming and being a liberal Democrat mutually exclusive?
not mutually exclusive
mutually exclusive
b) What is the probability that a randomly chosen respondent believes the earth is warming or is a liberal Democrat? (please round to four decimal places)
c) What is the probability that a randomly chosen respondent believes the earth is warming given that he is a liberal Democrat? (please round to four decimal places)
d) What is the probability that a randomly chosen respondent believes the earth is warming given that he is a conservative Republican? (please round to four decimal places)
e) Does it appear that whether or not a respondent believes the earth is warming is independent of their party ideology?
belief in global warming and party ideology are independent
belief in global warming and party ideology are dependent
Explanation / Answer
1)
a.the probability that a randomly selected peanut M&M is not Blue.
Solution : - P(not Blue ) = 1 - P(Blue) = 1 - 0.23= 0.77
b.the probability that a randomly selected peanut M&M is green or orange.
P(green)+P(orange)=0.15+0.23=0.38
c.the probability that three randomly selected peanut M&M’s are all yellow.
If the events are independent, the probability of both/all events occurring is determined by multiplying the probabilities of the individual events.
P(yellow)^3= (0.15)^3 =0.0034
d. For three peanut M&M’s, the probability that none of them are blue.
P(none blue)^3 = (1-0.23)^3 =0.4565
e.For randomly select three peanut M&M’s, the probability that at least one of them is blue is
“at least one" = 1, 2 or 3 are Blue .
P(Blue)^3 = (0.23)^3 = 0.0122
2)
d= depression , w:weight gain ,b= experience both
Suppose d=37% ,w=31%, b=17%.
a) 1-p(b) =1-0.17=0.83
b)P(d/w)=p( b)/ p(w) =0.17/0.31=0.5484
c) P(w/d)=P(b)/P(d) =0.17/0.37 =0.4595
d) No,depression and weight gain are not mutually exclusive.
Because probability that experience both is 0.17.
e) No,Are depression and weight gain not independent.
Because P(b) is not equal to p(d)+p(w)
3.)
a) not mutually exclusive
b) P(earth is warming or liberal Democrat) = P(earth is warming) + P(liberal Democrat) - P(earth is warming and liberal Democrat) = 0.60 + 0.20 - 0.18 = 0.62
(c) P(earth is warming — liberal Democrat) = 0.18 /0.9=0.20
(d) P(earth is warming — conservative Republican) = 0.11/0.33=0.33
(e) No, the two appear to be dependent. The percentages of conservative Republicans and liberal Democrats who believe that there is solid evidence that the average temperature on earth has been getting warmer over the past few decades are very different.
(f) P(moderate/liberal Republican — not warming) = 0.06/0.18 =0.34
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