Section3.3_ Probabilites Using Counting Methods.notebook
November 30, 2015
Section 3.3 Probabilities Using Counting Methods
Probability Using Counting Techniques
Some probabilities can be calculated using the three main counting techniques covered earlier.
These include:
• Fundamental Counting Principle
• Permutations
• Combinations
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Section3.3_ Probabilites Using Counting Methods.notebook
November 30, 2015
Fundamental Counting Principle
Many probability calculations rely on computing the number of choices for one item, followed by the number of choices for a second, and so on. The FCP is a useful tool for these situations.
Permutations
Some situations require specific orderings or rankings of items. Since order is important, permutations are used.
Combinations
Some probabilities are not influenced by ordering. For example, a question may ask about the probability of having a three­card hand in cards, or forming a committee. In these cases, combinations are applicable.
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Section3.3_ Probabilites Using Counting Methods.notebook
A.
November 30, 2015
Probabilities with Fundamental Counting Principle 1. Three people line up to buy a ticket at the movie theatre. What is the probability that they line up in descending order of age?
2. A financial institution randomly generates temporary three­digit security codes for the backs of credit cards. Tisa is expecting her credit card to arrive in the mail. Determine the probability that her security code will consist of three different odd digits.
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Section3.3_ Probabilites Using Counting Methods.notebook
November 30, 2015
3. A four digit pin number can begin with any digit, except 0, and the remaining digits have no restriction. If repeated digits are allowed, find the probability of the PIN code beginning with a number greater than 7 and ending with a 3.
Approach P(PIN CODE >7 __ __ 3 ) =
Pin Numbers greater than 7 ending in 3
Total Possible Pin Numbers
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Section3.3_ Probabilites Using Counting Methods.notebook
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4. A security code consists of 6 digits, which may be any number from 0 to 9. The code can begin with any digit except zero. No repetitions are allowed. Determine the probability that a particular code begins with an even digit.
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Section3.3_ Probabilites Using Counting Methods.notebook
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5. If a 4 digit number is generated at random from the digits 2, 3, 5, and 7 (without repetition of the digits), what is the probability that it will be even?
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Section3.3_ Probabilites Using Counting Methods.notebook
November 30, 2015
6. What is the probability that a randomly­selected Canadian postal code contains no two identical letters or digits?
7. Blake has three children. What is the probability that at least one is a boy? (Two methods)
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Section3.3_ Probabilites Using Counting Methods.notebook
November 30, 2015
8. Mark, Abby, and 5 other students are standing in line. A)
B)
Determine the probability Mark and Abby are standing together in the line.
The probability of them not together? 1­ Ans in A
Page 159 ­ 161: Questions 5, 9, 12, 16
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Section3.3_ Probabilites Using Counting Methods.notebook
November 30, 2015
Probabilities with Permutations
1. Nine students have a race. What is the probability of successfully predicting the three fastest runners?
2. From a committee of 10 people, 3 are randomly chosen to be president, secretary, and treasurer. Determine the probability that Kamal, Eli, and Salama will be chosen.
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Section3.3_ Probabilites Using Counting Methods.notebook
November 30, 2015
3. Dar spells out COOKBOOK with letter tiles. The tiles are face down and mixed up. He asks Devon to arrange the tile in a row and turn them face up. If the row of tiles spells COOKBOOK, Devon will win a series of gift cards for local restaurants. Determine the probability that Devon will win.
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Section3.3_ Probabilites Using Counting Methods.notebook
November 30, 2015
4. Access to a particular online site is password protected. Every member must create a password that consists of 3 capital letters followed by 2 digits. For each condition below, determine the probability that a password chosen at random will contain the letters A, B, and C.
a) Repetitions are not allowed in a password.
b) Repetitions are allowed in a password.
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Section3.3_ Probabilites Using Counting Methods.notebook
November 30, 2015
5. There are 3 different door prizes to be given out at an education conference. At the conference, there are 7 math teachers, 10 science teachers, 4 English teachers, and 8 social studies teachers. a) What is the probability all three prizes will be won by math teachers?
b) What is the probability all the prizes are won by teachers of the same subject area?
You could rephrase this question as : What is the probability all three prizes are won by only math teachers or only the science teachers or only social studies teachers or only English teachers.
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Section3.3_ Probabilites Using Counting Methods.notebook
November 30, 2015
Probabilities with Combinations
1. In the card game Crazy Eights, players are dealt 8 cards from a standard deck of 52 playing cards. Determine the probability that a hand will contain exactly 7 hearts.
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Section3.3_ Probabilites Using Counting Methods.notebook
November 30, 2015
2. A bookcase contains 6 different math books and 12 different physics books. If a student randomly selects two of these books, determine the probability they are both math or both physics books.
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Section3.3_ Probabilites Using Counting Methods.notebook
November 30, 2015
3. Steven, Brittany, Julie, and Max are volunteering along with five other students on their school’s math team. All the students have equal ability. Determine the probability that Steven, Brittany, Julie, and Max will be chosen to fill the five spots on the team.
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Section3.3_ Probabilites Using Counting Methods.notebook
November 30, 2015
4. Jarrod’s teacher has packs of 9 different colours of construction paper available: red, orange, yellow, green, blue, purple, pink, brown, and turquoise. She distributes 5 sheets of construction paper, each a different colour, to each student. Determine the probability that Jarrod will receive red, purple, and blue construction paper, along with two other colours. 16
Section3.3_ Probabilites Using Counting Methods.notebook
November 30, 2015
5. A jar contains 5 orange, 3 purple, 7 blue, and 5 green candies. If the total number of candies is 20, determine the probability that a handful of 4 candies contains one of each color.
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Section3.3_ Probabilites Using Counting Methods.notebook
November 30, 2015
6. Seven males and 9 females are in a selection pool for a committee of 4 people. What is the probability at most 2 males are on the committee?
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Section3.3_ Probabilites Using Counting Methods.notebook
November 30, 2015
7. Two students passed in their response to the following question. There are 7 teachers and 3 administrators at a conference. Find the probability of three different door prizes being awarded to teachers only.
(A) What does student's A equation represent?
(B) What does student's B equation represent?
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