In: Statistics and Probability

CALCULATING PROBABILITIES USING TREE DIAGRAMS AND COMBINATIONS

Two apples are chosen from a basket containing five red and three yellow apples. Draw a tree diagram below, and find the following probabilities.

1) P(one red, one yellow)

2) P(First red and second yellow)

Three marbles are drawn from a jar containing five red, four white, and three blue marbles. Find the following probabilities using combinations.

1) P(two white and 1 blue)

2) P(at least one red)

A committee of four is selected from a total of 4 freshmen, 5 sophomores, and 6 juniors. Find the probabilities for the following events.

1) No sophomores.

2) Not all four from the same class.

3) More juniors than freshmen and sophomores combined.

COMBINATIONS
Do the following problems using combinations.
1) How many different 5-player teams can be chosen from eight
players?
2) How many 13-card bridge hands can be chosen from a deck of
cards?
COMBINATIONS INVOLVING SEVERAL SETS
Following problems involve combinations from several different
sets.
1) A club has 4 men, 5 women, 8 boys and 10 girls as members. In
how many ways can a group of 2 men, 3 women, 4 boys and 4 girls be
chosen?
2)...

(b) In a new casino game, two balls are chosen randomly from an
urn containing 8 white, 4 black, and 2 orange balls to see if you
will win any money. Suppose that you win $2 for each black ball
selected, you lose $1 for each white ball selected, and you get
nothing for each orange ball selected. If the casino lets you play
this new casino game with no entry fee, what is the probability
that you will not...

Using well labelled diagrams, explain how the equilibrium price
and equilibrium quantity of apples will change as a result of the
following; 2.2.1 A change in the wages of farm workers from R150
per day to R200 per day. (10) 2.2.2 A decrease in the price of
fertilizers and a concurrent increase in the demand for apple
juice. (10)

Using well labelled diagrams, explain how the equilibrium price
and equilibrium quantity of apples will change as a result of the
following; 2.2.1 A change in the wages of farm workers from R150
per day to R200 per day. (10) 2.2.2 A decrease in the price of
fertilizers and a concurrent increase in the demand for apple
juice.

Two balls are chosen randomly from a box containing 8 white, 4
red, and 2 green balls to see if you will win any money. Suppose
that you win $2 for each red ball selected, you lose $1 for each
blue ball selected, and you get nothing for each green ball
selected. What is the probability that you will not lose any
money?

Q2. Two balls are chosen randomly from an urn containing 8
white, 4 black, and 2 orange balls. Suppose that we win $2 for each
black ball selected and we lose $1 for each white ball selected.
Let X denote our winnings. What are the possible values of X, and
what are the probabilities associated with each value i.e. create a
discrete probability distribution table for winning amount. Compute
the expected value of winnings and standard deviation of winnings.
You...

Using binomial and poisson distributions to find probabilities
using the two equations from binominal and poisson
An inspector looks for blemishes in the finish on porcelain and
counts the number of defects on batches of 12 vases. If the mean is
1.2, what is the probability he finds exactly one blemish?
(poisson)
A nail salon tracks the number of customers that enter each
minute. In an average minutes 0.35 customers enter. What is the
probability at least 1 customer enters...

Q.2 Using well labellled diagrams,explain how the equilibrum
price and and equilibrum quantity of apples will change as s result
of the following,
2.1 A change in the wages of farm woorkers from R150 per day to
R 200per day.
2.2 A Decrease in the price of fertilizers and a concurrent
increase in the demand of apple juice.

Suppose there is a basket containing one apple and two
oranges. A student randomly pick one fruit from the basket until
the first time the apple is picked. (Sampling with
replacement)
(a) What is the sample space for this experiment? What
is the probability that the student pick the apple after i
tosses?
(b) What is the expected number of times the students
need to pick the apple?
(c) Let E be the event that the first time an apple...

2.2 Using well labelled diagrams, explain how the equilibrium price and equilibrium quantity of apples will change as a result of the following;
2.2.1 A change in the wages of farm workers from R150 per day to R200 per day. (10)
2.2.2 A decrease in the price of fertilizers and a concurrent increase in the demand for apple juice. (10)

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