Module 6Hand-In Assignments1/7
Module 6 Lesson 2 Hand-In Assignment
Description
This is a hand-in assignment. It includes questions related to the previous lessons.
- Do all questions in Word.
- Organize your work as shown in the Exercise Answer Keys from previous lessons.
Be sure to name your Word file with a clearly understandable title and include your name in the title. For example: m6_l2_assignment_ima_student.doc
Note
Calculations in Word can be shown as follows:
P(of rolling a sum of 2):
= 1 : 36
= 1/36
= 0.027777…
= 2.7 %
Method of Evaluation
Refer to the “Hand-In Assignment Rubric” noted in the Introduction to this module. Your teacher may use this rubric or one similar when marking your hand-in assignment.
Directions for hand-in
Send the answers to your teacher as an attachment to an email message. Make the subject of the email "Module 6 Lesson 2 Assignment".
Questions
1.Two 6-sided dice are rolled and the sum of the values on the face of the dice is recorded. All possible sums are shown in the table below
1 / 2 / 3 / 4 / 5 / 6
First Dice / 1 / 2 / 3 / 4 / 5 / 6 / 7
2 / 3 / 4 / 5 / 6 / 7 / 8
3 / 4 / 5 / 6 / 7 / 8 / 9
4 / 5 / 6 / 7 / 8 / 9 / 10
5 / 6 / 7 / 8 / 9 / 10 / 11
6 / 7 / 8 / 9 / 10 / 11 / 12
a.How many possible sums are there?
b.Determine each of the following probabilities as a reduced fraction and as a decimal rounded to 3 decimal places.
i.P(sum is an even number)
ii.P(sum = 8)
iii.P(sum < 10)
iv.P(two odd numbers)
v.P(sum = 4)
c. If the pair of dice were rolled 100 times, how many times would a sum of 5 most likely appear?
d.If the pair of dice were rolled another 100 times, would the sum of 5 appear the same number of times as predicted in part (c)? Explain.
2. The probability of being born on Friday the 13th is 1 : 213. Based on this probability, how many people living in a town with a population of 4500:
a) would be expected to have been born on Friday the 13th?
b) would not have been born on Friday the 13th?
3.A Senior 3 math student surveyed students in her school by asking each person their age as they passed by her in the hallway. The results of her survey are shown in the following graph.
a.Calculate the total number of students surveyed.
b. What is the probability that a surveyed student is 16 years old?
c. What is the probability that a surveyed student is older than 18?
d.What is the probability that a surveyed student is not 20 years old?
e.Based on this survey, how many of the 600 students in the school are 20 years old?
e.If another Senior student conducted a similar survey at a different time and place, would the results be similar? Explain.
Module 6 Lesson 2 Hand-In Assignment Answer Key
1.a.There are 36 possible sums.
b.i.P(sum is an even number):
= 18/36
= 1/2
= 0.500
ii.P(sum = 8):
= 5/36
= 0.139
iii.P(sum < 10):
= 30/36
= 5/6
= 0.833
iv.P(two odd numbers):
= 9/36
= 1/4
= 0.25
v.P(sum = 4):
= 3/36
= 1/12
= 0.083
c. P(sum = 5):
= 4/36
= 1/9
Number of times 5 is expected to appear in 100 rolls:
= 1/9 x 100
= 11.11111…
= 11 times
d.If the pair of dice was rolled another 100 times, the sum of 5 may or may not appear the same number of times as in part (c). However, it should appear approximately the same number of times. The more often the dice are rolled, the closer will be the results will be to the predicted probability.
2. a) The number of people born on Friday the 13th:
= 1/213 x 4500
= 21.12676
= 21 (rounded to the nearest person)
b) The number of people not born on Friday the 13th:
= 4500 – 21
= 4479
3.a.The total number of students surveyed:
= 15 + 35 + 40 + 20 + 15 + 5
= 130
b. P(16 years old):
= 35/130
= 7/26
c. P(older than 18):
= 20/130
= 4/26
d.Number of 20 years olds = 5
Number not 20 years old = 125
P(student is not 20 years old);
= 125/130
= 25/26
e.P(20 years old):
= 1/26
Number of 20 year olds in the school:
= 1/26 x 600
= 23.076923…
= 23s (rounded to the nearest student)
e.Answers will vary.
Module 6 Lesson 4 Hand-In Assignment
Description
This is a hand-in assignment. It includes questions related to the previous lessons.
- Do all questions in Word.
- Organize your work as shown in the Exercise Answer Keys from previous lessons.
- If a spreadsheet is used, copy the completed spreadsheet and paste it into your Word document.
Be sure to name your Word file with a clearly understandable title and include your name in the title. For example: m6_l4_assignment_ima_student.doc
Note
Calculations in Word can be shown as follows:
P(of rolling a sum of 2):
= 1 : 36
= 1/36
= 0.027777…
= 2.7 %
Method of Evaluation
Refer to the “Hand-In Assignment Rubric” noted in the Introduction to this module. Your teacher may use this rubric or one similar when marking your hand-in assignment.
Directions for hand-in
Send the answers to your teacher as an attachment to an email message. Make the subject of the email "Module 6 Lesson 4 Assignment".
Questions
1.Lotteries are contests in which each entrant has an equal chance of winning the prize. For most lotteries, you can enter more than once. Suppose that you have entered two different lotteries, purchasing the number of tickets shown in the table below.
of Tickets / Total Tickets
Purchased
A / 5 / 175
B / 4 / 120
a.What is the probability of you winning Lottery A? (as a % rounded to 1 decimal)
b.What are the odds against you winning Lottery A?
c.What is the probability of you winning Lottery B? (as a % rounded to 1 decimal)
d.What are the odds against you winning Lottery B?
e.Which of the lotteries are you most likely to win? Explain.
2.The odds in favour of a family with three children having all girls are 1 to 7.
a.What is the probability of this event occurring?
b.If 100 three-children families were surveyed, how many of these would most likely have three girls?
3.A bag contains 20 marbles. There are five red, three black, two white, and the remainder are green. The game is played by drawing one marble from the bag. The characteristics of the game are:
- if you draw a red, you win $2.00
- if you draw a black, you win $3.00
- if you draw a white, you win $5.00
- if you draw a green, you win $0
- it costs $2.00 to play the game
a. Calculate the probability of each draw described above.
b.Calculate the expected value of this game and explain its meaning.
c.If you played this game 25 times, how much would you expect to win or lose?
Module 6 Lesson 4 Hand-In Assignment Answer Key
1.a.P(winning A):
= 5/175
= 1/35
= 0.0285714…
= 2.9%
b.The odds against winning Lottery A are 34 : 1.
c.P(winning B):
= 4/120
= 1/30
= 0.0333333…
= 3.3%
d.The odds against winning Lottery B are 29 : 1.
e.You are most likely to win Lottery B. The probability of winning B is approximately 0.4% higher. This is reflected in the lower odds against. (29 : 1 compared to 34 : 1).
2.a.P(of 3 girls) = 1 : 8.
b.Number of three-girl families in 100 three-girl families is:
= 1/8 x 100
= 12.5
Therefore, approximately 12 or 13 families would most likely have three girls.
3.a.P(drawing a red) = 5/20 or 1/4
P(drawing a black) = 3/20
P(drawing a white) = 2/20 or 1/10
P(drawing a green) = 10/20 or 1/2
b.
The expected value of the game is – $0.55. This means that if the game is played a number of times, you would lose on average $0.55 each time.
c.If you played the game 25 times, you would expect to lose:
= 25 x – $0.55
= – $13.75