Question

Recall the pre-lab candy situation consider: two unopened bags
of candy (one Skittles the other M&M's). The manufacturers
state the distribution of coloured candies is:

M&M'S MILK CHOCOLATE: 24% blue, 19% orange, 16% green, 13%
yellow, 13% red, 15% brown.

SKITTLES: colours are reportedly distributed evenly, meaning each
colour (red, orange, green, blue, yellow, and purple) has a
probability of 1616.

Assume that both of these unopened bags have the same number of
candies. If they are opened and mixed, and one candy is randomly
selected; what is the probability it is a Skittle? [Hint: only
focus on the colour you need]

?(Skittle | blue)= ????

Answer #1

P(Skittle) = 0.5

P(M&M) = 0.5

P(blue | Skittle) = 0.16

P(blue | M&M) = 0.24

P(blue) = P(blue | Skittle) * P(Skittle) + P(blue | M&M) * P(M&M)

= 0.16 * 0.5 + 0.24 * 0.5

= 0.2

P(Skittle | blue) = P(blue | Skittle) * P(Skittle) * P(blue) =
0.16 * 0.5 / 0.2 = **0.4 (ans)**

Probability that the candy selected is a skittle = 0.5

Upon request, the Mars Company (the maker of M&M's) will
provide the color distribution for their candies. As of August
2009, they noted that
"Our color blends were selected by conducting consumer
preference tests, which indicate the assortment of
colors
that pleased the greatest number of people and created the most
attractive overall effect.
On average, our mix of colors for M&M'S CHOCOLATE CANDIES
is:
M&M'S MILK CHOCOLATE: 24% cyan blue, 20% orange, 16% green,
14% bright yellow, 13% red,...

M&M plain candies come in various colors. According to the
M&M/Mars Department of Consumer Affairs, the distribution of
colors for plain M&M candies is as follows. Color Purple Yellow
Red Orange Green Blue Brown Percentage 19% 17% 22% 10% 6% 8% 18%
Suppose you have a large bag of plain M&M candies and you
choose one candy at random. (a) Find P(green candy or blue candy).
Are these outcomes mutually exclusive? Why? No. Choosing a green
and blue M&M is...

M&M's Color Distribution: Suppose the
makers of M&M candies give the following average percentages
for the mix of colors in their bags of plain chocolate
M&M's.
Stated Distribution of Colors
Brown
Yellow
Red
Orange
Green
Blue
Percent
30%
20%
20%
10%
10%
10%
Now, you randomly select 200 M&M's and get the counts given
in the table below. You expected about 20 blues but only got 9. You
suspect that the maker's claim is not true.
Observed Counts by Color...

In a bag of M & M's, there are 80 M & Ms, with 11 red
ones, 12 orange ones, 20 blue ones, 10 green ones, 18 yellow ones,
and 9 brown ones. They are mixed up so that each candy piece is
equally likely to be selected if we pick one.
( ALL ANSWERS ROUNDED TO THREE DECIMAL PLACES)
a) If we select one at random, what is the probability that it is
yellow?
P(Yellow) ______________
b) If we...

M&M's Color Distribution: Suppose the
makers of M&M candies give the following average percentages
for the mix of colors in their bags of plain chocolate
M&M's.
Stated Distribution of Colors
Brown
Yellow
Red
Orange
Green
Blue
Percent
30%
20%
20%
10%
10%
10%
Now, you randomly select 200 M&M's and get the counts given
in the table below. You expected about 20 blues but only got 9. You
suspect that the maker's claim is not true.
Observed Counts by Color...

M&M's Color Distribution: Suppose the
makers of M&M candies give the following average percentages
for the mix of colors in their bags of plain chocolate
M&M's.
Stated Distribution of Colors
Brown
Yellow
Red
Orange
Green
Blue
Percent
30%
20%
20%
10%
10%
10%
Now, you randomly select 200 M&M's and get the counts given
in the table below. You expected about 20 blues but only got 9. You
suspect that the maker's claim is not true.
Observed Counts by Color...

M&M's Color Distribution: Suppose the
makers of M&M candies give the following average percentages
for the mix of colors in their bags of plain chocolate
M&M's.
Stated Distribution of Colors
Brown
Yellow
Red
Orange
Green
Blue
Percent
30%
20%
20%
10%
10%
10%
Now, you randomly select 200 M&M's and get the counts given
in the table below. You expected about 20 blues but only got 10.
You suspect that the maker's claim is not true.
Observed...

According to M&Ms Web site, each package of the milk
chocolate candies typically contain 14% brown, 13% red, 14% yellow,
16% green, 24% blue, and 20% orange M&Ms. You go to the store
and buy a standard-sized package. When you open it, you find that
it contains 51 M&Ms, distributed as follows: Color Brown Red
Yellow Green Blue Orange Frequency 8 4 10 4 11 11 Over the long
run, what is the probability that the first M&M you select...

During summer vacation, a babysitter gives some kids snack size
bags of M&M's. She wonders if the candy color distribution in
each snack bag matches the distribution of colors reported online
that says 24% blue, 13% brown, 16% green, 20% orange, 13% red, and
14% yellow. She has the kids count what they observe in their snack
bags. She does a test and the P-value= 0.024. She used a 5% level
of significance.
(Do Not Perform The Tests! Just answer...

The Mars company says, that before the introduction of purple,
yellow made up 20% of their plain M&M candies, red made up
another 20%, and orange, blue, and green each made up 10%. The rest
were brown. Assuming you had an infinite supply of M&M's with
the older color distribution, if you picked six M&M's in a row,
what is the probability that at least one is brown?
Do not round intermediate calculations. Round your final answer
to four decimals.

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