Name ______Unit 8–Basic Concepts Continued

DAY 3 - Basic Concepts of Probability Continued

RECAP:

1. Any probability is a number between 0 and 1 (inclusive).

The probability P(A) of any event A satisfies ______.

2. Law of Large Numbers

3. Tree diagrams

4. Outcomes, sample space, events (including simple event)

5. Formal or theoretical probability vs. experimental or empirical probability

NOTATION: ______.

REMEMBER: ______.

If S is the sample space in a probability experiment, then P(S) = 1.

More Key Terms

Complementary Events - ______.

  • ______

**This is like finding how much of the normal curve is shaded to the right (1 - %)**

The probability that an event does not occur (its complement) is 1 minus the probability that the event does occur:

For any event A: ______

Example 1:

Suppose you roll a six-sided die. Let A be the event that you roll at least a four.

1. What are the possible rolls for the probability experiment?

2. What is the complement of A? (A' or Ac)

3. What is the P(A)? P(A')?

4. What is P(A)+P(A')?

Example 2:

Suppose we run another probability experiment where we roll two six-sided dice. Let B be the event that we roll doubles, like 1 and 1.

What is the probability of not rolling doubles? First write this probability using proper notation, then calculate using the probability rules we have learned.

Example 3:

What is the probability a person did not get between 31-35 marks? Let C be the event that a person did get between 31-35 marks. Be sure to write your solution with proper probability notation.

Example 4 (Introduction to Combinations & Permutations):

The access code for a car's security system consists of four digits.

Each digit can be any number from 0 to 9.

How many codes are possible if:

a) each digit can be only used once and not repeated?

b) each digit can be repeated?

c) each digit can be repeated, but the first digit cannot be 0 or 1?

d) each digit cannot be repeated, and the first digit cannot be 0 or 1?

Exit Ticket (Turn in this page ONLY):

1. Canada has two official languages, English and French. Choose a Canadian at random and ask, "What is your mother tongue?" Here is the distribution of responses, combining many separate languages from the broad Asian/Pacific region:

(a) What probability should replace "?" in the distribution?

(b) What is the probability that a Canadian's mother tongue is not English?

2. A probability experiment consists of tossing a coin, and spinning the spinner shown. The spinner is equally likely to land on each number.

Create a tree diagram to give the sample space of this experiment.

Use your tree diagram to determine the probability of each event.

Event A: Tossing a tail and spinning an odd number: ______

Event B: Tossing a head and spinning a number greater than 3: ______

Event C: Tossing a tail and spinning a prime number: ______