Question

Part A: Answer all the questions below. You are required to
number all your answers correctly and write all the necessary
solutions in your answer sheets.

1. If you would win $25 if you pulled a heart from a standard
deck of 52 cards, the Expected Monetary Value would be? Write the
implications if this bet is repeated a large number of times. [3
Marks]

2.
Ifan8-characterPINisselectedfrom0,1,2,3,4,5,6,7,8,9,X,P,Rwhatisthetotal
possible number of PINs without repetitions? [2 Marks]

3. How many total number of combinations without repetition
has the set A = {2, 5, 9, 3, 7, 8, 1, 6} if you choose 4? [2
Marks]

4. If a box has 14 red, 300 blue, 5 green, and 2 black
marbles, find the probability that a marble is not green if a
marble is selected randomly. [2 Marks]

5. If a die is rolled, what is the probability of randomly
getting a number greater than 4 or an even number?. [2.5
Marks]

Answer #1

A jar contains 5 red, 9 blue, and 6 green marbles. You randomly
select three marbles from the jar, without replacement.
1. Find the probability of selecting three blue marbles.
2. Find the probability of selecting a marble of each color.
3. Would it be more appropriate to use combinations or permutations
to solve this problem?
4. Find the probability of selecting three red marbles.
5. Find the probability of selecting three green marbles.
6. Find the probability of selecting...

X
P(X=x)
Geoff is running a carnival game. He has 15 marbles in a bag:
there are 4 green marbles, 7 red marbles and 4 yellow marbles. To
play a round of the game, a player randomly takes out a marble from
the bag, notes the color and replaces it, then pulls a second
marble from the bag and notes the color. So in effect, the player
pulls 2 marbles from the bag. (However, the first marble is put
back...

An urn contains ten marbles, of which 4 are green, 3 are blue,
and 3 are red. Three marbles are to be drawn from the urn, one at a
time without replacement.
(a) Let ?? be the event that the ?th marble drawn is green. Find
?(?1 ∩ ?2 ∩ ?3), which is the probability that all three marbles
drawn are green. Hint: Use the Multiplicative Law of
Probability
(b) Now let ?? be the random variable defined to be...

Q1.
Part a) A bag contains 12 marbles. There are 4 marbles that are
pink, 5 are purple, and 3 are blue. A marble is randomly pulled out
of the bag. What is the probability that the marble selected is
pink or blue? Round to 4 decimals.
Part b) A student randomly guesses on a 20 question true/false
test. What is the probability that the student guesses correctly on
15 of the questions? Round to 4 decimals.
Part c) A...

3) Two cards are drawn from deck, with replacement. (This means
that one person chooses a card,looks at it and returns it, and then
another person chooses a card, looks at it, and returns it.) What
is the probability that ...
(a) ... the first card is an ace and the second card is
black?
(b) ... both cards are spades?
(c) ... neither card has a value from {2, 3, 4, 5}?(d) ... at
least one card is an...

Suppose you roll, two
6-sided dice Write any probability as a decimal to three place
values and the odds using a colon. Determine the following:
1. The probability
that you roll a sum of seven (7)
2. The odds for
rolling a sum of four (4) is
3. The odds against
the numbers on both dice being the same is
Suppose you have a bag
with the following marbles: four (4) red, six (6) pink, two (2)
green, and seven...

7. Events A and B are independent. The P(A) = 3/5, P(not B) =
2/3. What is P(A and B)? a. 2/5 b. 1/5 c. 4/15 d. 2/15
8. A bag contains 4 red marbles, 3 blue marbles, and 7 green
marbles. If a marble is randomly selected from the bag, what is the
probability that it is blue? A) 1/11 B) 3/14 C) 1/7 D) 1/3
9. The distribution of the heights of students in a large class
is...

Question 2
Please put your answer in fraction form, fully reduced. Ex.
5/12
If a die is rolled one time, find this probability:
Of getting an odd number
Question 3
If a die is rolled one time, find this probability:
Of getting a 4 or an odd number
Question 4
Please put your answer in fraction form, fully reduced. Ex.
5/12
If a die is rolled one time, find this probability:
Of getting a number greater than or equal...

Part 1: Answer these three questions inside of your Word
document file: 1. What is a confidence interval? 2. Provide an
example of a confidence interval? 3. Why do we need confidence
intervals in statistics? Additional information before your start
Part 2: Please use the below formula in Excel for developing the
combination calculation i.e., the number of ways of choose n
numbers k at a time…The Excel formula is =COMBIN(n,k). This will
tell you the number of combinations given...

Suppose that a drawer contains 8 marbles: 2 are red, 2 are blue,
2 are green, and 2 are yellow. The marbles are rolling around in a
drawer, so that all possibilities are equally likely when they are
drawn. Alice selects marbles (without replacement) until she gets a
red marble, and then she stops afterwards. Let X denote the number
of draws that are needed until the first red appears.
a. Find P(X=1).?
b. Find P(X=2).?
c. Find P(X=3).?
d....

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