Events Involving NOT and OR, Odds

​Events Involving NOT and OR; ODDS

​Applied Math

​Probability of an Event NOT occuring

P(E) + P(not E) = 1

​The event not E is the COMPLEMENT of E because it is the set of all outcomes in the sample space S that are not outcomes in the event.

The complement rule of probability is

P(not E) = 1 - P(E)

P(E) = 1 - P(not E)

​Example

​If you are dealt one card from a standard 52 card deck, find the probability that you are not dealt a queen.

​Because P(not E) = 1-P(E)

Then P (not a queen) = 1 - P(queen)

4/52 = 1/13 1 - 1/13 = 13/13 - 1/13 = 12/13

Multiple Choice

If the spinner is spun one time, what is the probability of the arrow not landing on a section labeled with an odd number?

• $$\frac{4}{7}$$

• $$\frac{3}{4}$$

• $$\frac{1}{4}$$

• $$\frac{3}{7}$$

Multiple Choice

The table shows the types of movies and the number of DVDs rented by customers at a store in one day. Based on the data in the table, what is the probability that a random customer will not rent a drama?

• $$\frac{1}{4}$$ , because the probability of renting a drama is $$\frac{3}{4}$$

• $$\frac{3}{4}$$ , because the probability of renting a drama is $$\frac{1}{4}$$

• $$\frac{4}{5}$$ , because the proability of renting a drama is $$\frac{1}{5}$$

• $$\frac{1}{5}$$ , because the probability of renting a drama is $$\frac{4}{5}$$

Multiple Choice

Lexi purchases a bag of assorted candies and discovers that out of the 32 pieces, 11 are butterscotch and 10 are cinnamon flavored. If Lexi selects a candy at random, what is the probability that the candy will not be butterscotch or cinnamon flavored?

• $$\frac{11}{32}$$

• $$\frac{11}{16}$$

• $$\frac{1}{2}$$

• $$\frac{21}{32}$$

​Probabilities with Mutually Exclusive Events

​If it is impossible for events A and B to occur simultaneously, the events are said to be Mutually Exclusive

​P(A or B) = P(A) + P(B)

P ( A U B) = P(A) + P(B)

​Example

​If one card is randomly selected from a deck of cards what is the probability of selecting a king or queen?

​P (King or Queen) = P(King) + P(Queen)

4/52 + 4/52 = 8/52 = 2/13

Multiple Choice

If you draw one card from a standard deck, what is the probability of drawing a spade or a red card?

• 1/4

• 1/2

• 3/4

• Not possible

• 3/5

Multiple Choice

If you roll one die, what is the probability of getting an odd number or a 4?

• 2/3

• 1/3

• 1/2

• 1/6

• 5/6

Multiple Choice

If you roll one die, what is the probability of getting an even number or a multiple of 3?

• 1/3

• 2/3

• 1/2

• 1/6

• 1/4

Fill in the Blanks

​Or Probability with Events that are NOT Mutually Exclusive

​If A and B are not mutually exclusive then

P(A or B) = P(A) + P(B) - P(A and B)

Using set notation

P(A U B) = P(A) + P(B) - P (A ⋂ B )

Multiple Choice

What are non mutually exclusive events?

• Events that can happen at the same time

• Events that cannot happen at the same time

• Events that add up to 100%

​Probability of odds

​Example

​You roll a single number cube

a. Find the odds in favor of rolling a 2

b. Find the odds in favor against rolling a 2

a. b.

Multiple Choice

The odds of an event happening are 3:8. What are the odds it does not happen?

• 8:3

• 3:11

• 11:3

• 8:11

Multiple Choice

An impossible event has a probability of _____?

• 1

• 0

• 1/2

• 100

Multiple Choice

The probability of the box having a toy is 6/13. What are the odds against the box having a toy?

• 7:13

• 6:7

• 7:6

• 13:6

Multiple Choice

The chance of rolling a 2 is 1/6. What is the chance of not rolling a 2?

• 2/6

• 1/6

• 5/6

• Not possible

Poll

I can solve any problems using NOT and OR, also ODDS?