Fill in Multiple
BlanksUse the set
definitions A = {a, b} and B = {b, c} to express the elements in
the power set P(A ∪ B).Use {} for the empty setDo not add any spaces in your answer. Example {f} not { f } {e,f,g} not {e, f, g}{[1],[2], [3], [4],
{a,b}, {b,c}, [5], [6]}
(5 pts) Suppose that the five standard Skittles colors (red,
orange, yellow, green, purple) occur with equal relative frequency.
Use the random digits below to simulate the colors of 4 randomly
selected Skittles. Continue to do this until you have generated 12
such samples of 4 Skittles. Use the results of these simulations to
approximate that probability that a sample of 4 Skittles will
contain at least two Skittles of the same color.
28491 06339 65216 31007 92314 50271
82943...
Brian is selling balloons in 8 different colours: red, pink,
yellow, blue, green, purple, black and silver.
How many different selections of 16 helium balloons can be
purchased if the shop has at least 16 balloons of each colour in
stock?
How many different selections of 16 helium balloons can be
purchased if you buy at least 3 red balloons and at least 5 yellow
balloons, and the shop has at least 16 balloons of each colour in
stock?
How...
A bag contains 4 red
marbles, 2 green ones, 2 white ones, and 1 purple one. Michelle
reaches into the bag and grabs 5 of the marbles.
1) Find the
probability that she has 2 red ones and 1 of each of the other
colors.
2) Find the
probability that she has at least 1 green marble.
Express your
answers as simplified fractions using the forward slash. Ex:
1/2
Red
Orange
Yellow
Green
Purple
Total
1046.
1066
977
1029
969
5087
Suppose all of the Skittles in the class data set are combined
into one large bowl and you are going to randomly select ten
Skittles with replacement and count how many are yellow.
(a) List the requirements of the binomial probability
distribution and show that this meets them, including identifying
the values for n and p. (6 points)
(b) What is the probability that exactly 4 of...
A shop sells helium balloons in eight different colours: red,
pink, yellow, blue, green, purple, black and silver. (a) How many
different selections of 16 helium balloons can be purchased if the
shop has at least 16 balloons of each colour in stock? (b) How many
different selections of 16 helium balloons can be purchased if you
buy at least 3 red balloons and at least 5 yellow balloons, and the
shop has at least 16 balloons of each colour...
Consider the following dataset:
x1 Yellow Yellow Green Green Red Red Green Red Yellow
x2 5 2 10 4 3 7 2 5 4
y 1 3 7 5 10 18 4 8 3
(a) (3pts) Split the data into a train and test set where the
test set contains observations 1 and 7. Answer this by writing down
the two datasets.
(b) (2pts) Use Rstudio to estimate a model (which uses both x1
and x2 as predictor variables) using...
Urn A contains 5 green and 4 red balls, and Urn B contains 3
green and 6 red balls. One ball is drawn from Urn A and transferred
to Urn B. Then one ball is drawn from Urn B and transferred to Urn
A. Let X = the number of green balls in Urn A after this process.
List the possible values for X and then find the entire probability
distribution for X.
Urn A contains 5 green and 4 red balls, and Urn B contains 3
green and 6 red balls. One ball is drawn from Urn A and transferred
to Urn B. Then one ball is drawn from Urn B and transferred to Urn
A. Let X = the number of green balls in Urn A after this process.
List the possible values for X and then find the entire probability
distribution for X.