You must demonstrate in your project write up that you have understood the following concepts involved in the section 'probability'.
(i) Probability definition: theoretical and experimental
(ii) Mutually exclusive events
(iii) Complimentary events
(iv) Dependent and independent events
(v) The meaning of 'and' versus 'or' in calculating probabilities
(vi) 4 probability equations : (1) P(A or B) = P(A) + P(B) - P(A and B) ; (2) P(A and B) = 0 (3) P(A and B) = P(A) × P(B) ; (4) P(A) = 1 - P(A)
(vii) The Counting Principle
(viii) The use of factorials
To assist you to explain the concepts, you must use at least one Tree Diagram and at least one Venn Diagram.
You must log on to Google Classroom and watch the YouTube clips to improve your understanding of the various probability concepts.
Your project must have a title page, and the rubric must be stuck onto this title page.
You must answer the compulsory questions at the end and then use the other problem examples given, to demonstrate an understanding of the concepts listed above, by giving a detailed solution to each problem, using any appropriate diagrams.
You must reference any other sources you use in your write up.
LIST OF PROBLEMS :
*Use the problems listed below. You may also use other problems you have found.
*Each of the 8 concepts listed above, must have at least 2 problem situations with clear write ups, to demonstrate your understanding of the concept.
PROBLEMS
1) In a raffle at VGHS to raise money for Child Welfare, 4500 tickets are sold. Determine the probability of winning the raffle if you purchase (a) 1 ticket (b) 10 tickets.
2) At a traffic light, the light is red for 30 seconds, orange for 5 seconds and green for 45 seconds. What is the probability you will arrive when the light is red?
3) A roulette wheel has 38 numbers : 1 to 36, 0 and 00. What is the probability that the roulette ball will come to rest on an even number other than 0 and 00?
4) A dart board consists of a circle divided into 20 equal parts. Find the probability of landing on
(a) a white sector
(b) a number divisible by 5
5) Boxes of eggs are inspected routinely to test for breakages.
The results of 10 checked boxes are : 5% had at least 3 eggs broken; while 15 % had no more than 2 eggs broken.
(a) Describe the possible outcomes of these findings.
(b) What is the probability that more than 2 eggs were broken in 10 boxes?
6) A 6 sided die and a 4 numbered spinner are shown.
The die is rolled and the pointer on the spinner is rotated. Find the probability that
(a) Doubles come up
(b) The sum of the numbers is greater than 7
(c) The sum of the numbers is not greater than 7.
7) A couple decide to have 3 children.
(a) Show the possible outcomes, if having a boy or a girl, is equally likely.
(b) Find the probability that
(i) all the children are girls (ii) at least one girl is born.
8) S = { 1; 2; 3; 4; 5; 6; 7; 8) A = (2; 3; 5; 6) B = (3; 4; 5; 7) C = {5; 6; 7; 8}
Find the probability of selecting a number
(a) In A and B
(b) In A or C
(c) In A and B and C
(d) In A or B but not C
9) A card is drawn from a pack of cards, replaced, and a second card is drawn.
Find the probability that
(a) both cards are clubs or both are diamonds
(b) both cards are red and both cards are 2s.
10) Is it possible for mutually exclusive events to be independent? Explain.
11) A snap revision quiz in Geography consists of 5 true/false questions. You are not prepared, so you guess every answer.
What is the probability you will get
(a) 100% ?
(b) At least one answer correct?
12) In a hotel in Hong Kong, the room keys are cards. Each card has positions for holes that form a 5 by 3 array. Each position in the array is either punched with a hole or left blank.
How many different keys are possible?
13) 60% of young drivers take driving lessons, and 25% of young drivers have an accident in their first year of driving. 10% of young drivers who take lessons have an accident in their first year.
Are taking driving lessons and having an accident in the first year independent events? Support your answer with appropriate calculations.
14) The probability that a VG Gr 12 pupil completes her maths homework is 0,6 :). The probability that she completes her Art assignment is 0,4. :(. If these events are independent, what is the probability that
(a) she completes both her Maths and Art? :)
(b) she completes neither? :(:(
15) Design a menu which has a selection of mains and sweets so that customers have a possible 20 choices of 2 course meals.
Show all working, necessary diagrams, calculations.
16) Consider the word FLORIDA.
(a) How many different arrangements of the 7 letters can be made if
(i) The letters may be repeated?
(ii) The letters may not be repeated?
(b) How many different arrangements can be made if only 4 letters are used if
(i) The letters may be repeated?
(ii) The letters may not be repeated?
17) Consider the word NEED. How many different arrangements of the letters can be made?
18) Consider the word KNIGHT.
How many arrangements can be made of the letters if the words must start with K?
19)
(a) In how many ways can 3 boys and 2 girls sit in a row?
(b) In how many ways can they sit in a row if the 2 girls want to sit together?
(Hint : draw diagrams!)
20) You must design a password system for the new Grade 8s to login to a game site in the computer labs.
The password must consist of 6 characters.
The password must start with 3 letters of the alphabet (no repetitions allowed)
The 4th and 5th characters must be a number from 0 - 9 (no repetitions allowed) (see below)
The 6th character must be one of the following symbols : # ; % ; & ; *
81 login numbers must be multiples of 2
82 login numbers must end in 0
83 login numbers must start with 1 or 2.
Show your working in the design of the passwords and give the total number of passwords possible for each Grade 8 set. Show all necessary calculations!