35/100=7/20

100 people were surveyed for their favorite fast-food restaurant.

1. What is the probability that a person likes Wendy’s?

2. What is the probability that a person is male who likes Burger King?

3. What is the probability that a person is likes McDonald’s or Burger King?

15/100 = 3/20

McDonald’s Burger King Wendy’s

Male 20 15 10

Female 20 10 25

65/100 = 13/20

Understanding the difference between dependent and independent events

If the outcome of the first event does not affect the possible outcomes of the second event, the events are called independent events.

If two events are independent, you can use this formula to find the probability of both events occurring.

P(A and B) = P(A) • P(B)

Understanding how to find the probability of events

The probability of an event is the ratio of the number of favorable outcomes to the number of possible outcomes.

number of favorable outcomes

number of possible outcomes

P(event) =

A simple event in a probability experiment is determined by the outcome of one trial in the experiment.

The probability of a compound event is the combination of at least two simple events.

Probability of Compound Events

• A compound event consists of two or more simple events.

• Examples: rolling a die and tossing a penny spinning a spinner and drawing a card tossing two dice

tossing two coins

Is this independent or dependent?• If we toss two coins, what is the probability of getting two

heads in a row? Make a tree diagram.

• Now what if we toss three coins, what is the probability of getting three heads in a row?

½ x ½ x ½ = 1/8

Why are we adding on this problem instead of multiplying

• A box contains three glazed doughnuts, four jelly doughnuts and five chocolate doughnuts. If a person selects a doughnut at random, find the probability that it is either a glazed doughnut or a chocolate doughnut.

• P(glazed or chocolate) = P(glazed) + P(chocolate)

= (3/12) + (5/12) = 8/12

A probability experiment consists of rolling a fair number cube numbered 1 through 6 and then spinning a spinner with two equally likely outcomes, red or blue. Find the probability of rolling a 2 on the number cube and spinning red on the spinner.

A bag contains 6 blue marbles, 4 red marbles, and 2 green marbles. One marble is drawn from the bag, and its color is recorded. Another marble is drawn, and its color is also recorded. What is the probability of drawing 2 blue marbles if the first marble is not returned to the bag before the second marble is drawn?

1/6 1/2 = 1/ 12 ∙

1/2 5/11 = 5/ 22 ∙

Suppose you roll a red number cube and a blue number cube. What is the probability that you will roll a 5 on the red cube and a 1 or 2 on the blue cube?

1/6 2/6 = 2/36 = 1/18 ∙

You toss a coin with two sides, heads and tails. Then you choose a block from a bag that has three blocks- one red, one green and one blue. What is the probability that you will toss a heads and then a blue block?

1/2 1/3 = 1/6 ∙

You pick a color from a set of crayons consisting of an equal amount of only red, yellow, and blue. Then you toss a die. Separately, each of these events is a simple event and the selection of a color does not affect the tossing of a die. What is the probability of picking a red crayon and rolling a 5?

(red and 5) (red) (5)P P P

1 1 1

3 6 18

This can be illustrated using a tree diagram to get a better understanding.

Since there are three choices for the color and six choices for the die, there are eighteen different results. Out of these, only one gives a combination of red and 5. Therefore, the probability of picking a red crayon and rolling a 5 is given by:

(red and 5) (red) (5)P P P 1 1 1

3 6 18

Or 3 x 3 x 2 = 18

How many different combinations can you come up with?

•Skills Check!When you finish turn your paper over, put it

in the corner of your desk and work on your practice.

Practice: Probability Worksheet

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