09 Oct STAT 2001 ? Statistics Assignment 1.STAT 2001 ? Statistics Assignment 1.
STAT 2001 – Statistics Assignment 1.
STAT 2001 – Statistics Assignment 1.
• Your solutions to the assignment should be placed in the appropriate box in the FAS School foyer by 1200 noon, Wednesday 25 March (Week 6). • The assignment is out of 20 and is worth 10% of your overall course mark. • Each part of each problem is worth 1 mark, except for Problem 6 which is worth 5 marks. • The assignment is to be done alone. Marks may be deducted for any copying. STAT 2001 – Statistics Assignment 1.
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Problem 1 (3 marks)
A die with 1, 1, 1, 2, 2 and 3 printed on its six faces is rolled twice. We observe the pair (i,j) where i and j are the numbers obtained on the 1st and 2nd rolls, respectively.
(a) Write down the sample space for this experiment.
(b) Assign probabilities to the simple events.
(c) Hence or otherwise, find the probability of obtaining exactly one 1 on the two rolls or a 3 on the second roll.
Problem 2 (3 marks)
Find the probability that 20 rolls of a fair die will yield: (a) three 6’s (b) at least one 6 (c) three 4’s, two 5’s and a 6.
STAT2001 Assignment 1 (2015) Problems.doc Page 2 of 3
Problem 3 (3 marks)
A teacher has 5 chocolates, 4 lollies and 3 licorice sticks to distribute to a class of 14 pupils. No pupil may get more than one item, and all the items must be given out. The chocolates are all alike, as are the lollies and the licorice sticks.
(a) In how many ways can the items be distributed amongst the class (without regard to the order in which this is done)? STAT 2001 – Statistics Assignment 1.
(b) In how many ways can the items be distributed amongst the class, taking into account the order in which this is done?
(c) If the items are distributed at random, what is the probability that John, Joe and Jim will get the same item whilst Jenny gets a chocolate?
Problem 4 (3 marks)
A bag initially contained 4 white marbles and 9 black marbles. A marble was drawn and replaced by two marbles of the opposite colour. Then another marble was drawn and also replaced by two marbles of the opposite colour. A third marble was then drawn.
STAT 2001 – Statistics Assignment 1.
Find the probability that the first marble drawn was white if:
(a) the second marble drawn was white
(b) the third marble drawn was white
(c) both the second and third marbles drawn were white.
STAT2001 Assignment 1 (2015) Problems.doc Page 3 of 3
Problem 5 (3 marks)
Players A and B take turns at rolling two dice, starting with A. The first person to get a sum of at least 9 on a roll of the two dice wins the game.
Find the probability that A will win the game if:
(a) the game is just about to begin
(b) 8, 4, 3, 7 and 7 have already been rolled
(c) a draw is to be declared in the event of no-one winning within 6 rolls.
Problem 6 (5 marks)
Suppose that you have 20 different letters and 10 distinctly addressed envelopes. The 20 letters consist of 10 pairs, where each pair belongs inside one of the 10 envelopes. Suppose that you place the 20 letters inside the 10 envelopes, two per envelope, but at random.
What is the probability that exactly 3 of the 10 envelopes will contain both of the letters which they should contain? STAT 2001 – Statistics Assignment 1.
STAT 2001 – Statistics Assignment 1.
• Your solutions to the assignment should be placed in the appropriate box in the FAS School foyer by 1200 noon, Wednesday 25 March (Week 6). • The assignment is out of 20 and is worth 10% of your overall course mark. • Each part of each problem is worth 1 mark, except for Problem 6 which is worth 5 marks. • The assignment is to be done alone. Marks may be deducted for any copying. STAT 2001 – Statistics Assignment 1.
Permalink: https://collepals.com//stat-2001-statistics-assignment-1/
Problem 1 (3 marks)
A die with 1, 1, 1, 2, 2 and 3 printed on its six faces is rolled twice. We observe the pair (i,j) where i and j are the numbers obtained on the 1st and 2nd rolls, respectively.
(a) Write down the sample space for this experiment.
(b) Assign probabilities to the simple events.
(c) Hence or otherwise, find the probability of obtaining exactly one 1 on the two rolls or a 3 on the second roll.
Problem 2 (3 marks)
Find the probability that 20 rolls of a fair die will yield: (a) three 6’s (b) at least one 6 (c) three 4’s, two 5’s and a 6.
STAT2001 Assignment 1 (2015) Problems.doc Page 2 of 3
Problem 3 (3 marks)
A teacher has 5 chocolates, 4 lollies and 3 licorice sticks to distribute to a class of 14 pupils. No pupil may get more than one item, and all the items must be given out. The chocolates are all alike, as are the lollies and the licorice sticks.
(a) In how many ways can the items be distributed amongst the class (without regard to the order in which this is done)? STAT 2001 – Statistics Assignment 1.
(b) In how many ways can the items be distributed amongst the class, taking into account the order in which this is done?
(c) If the items are distributed at random, what is the probability that John, Joe and Jim will get the same item whilst Jenny gets a chocolate?
Problem 4 (3 marks)
A bag initially contained 4 white marbles and 9 black marbles. A marble was drawn and replaced by two marbles of the opposite colour. Then another marble was drawn and also replaced by two marbles of the opposite colour. A third marble was then drawn.
STAT 2001 – Statistics Assignment 1.
Find the probability that the first marble drawn was white if:
(a) the second marble drawn was white
(b) the third marble drawn was white
(c) both the second and third marbles drawn were white.
STAT2001 Assignment 1 (2015) Problems.doc Page 3 of 3
Problem 5 (3 marks)
Players A and B take turns at rolling two dice, starting with A. The first person to get a sum of at least 9 on a roll of the two dice wins the game.
Find the probability that A will win the game if:
(a) the game is just about to begin
(b) 8, 4, 3, 7 and 7 have already been rolled
(c) a draw is to be declared in the event of no-one winning within 6 rolls.
Problem 6 (5 marks)
Suppose that you have 20 different letters and 10 distinctly addressed envelopes. The 20 letters consist of 10 pairs, where each pair belongs inside one of the 10 envelopes. Suppose that you place the 20 letters inside the 10 envelopes, two per envelope, but at random.
What is the probability that exactly 3 of the 10 envelopes will contain both of the letters which they should contain? STAT 2001 – Statistics Assignment 1.
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