Lesson 7.6: Find Probabilities of Compound Events

Probabilities of Compound Events

Some text here about the topic of discussion

Key Concept:

Finding the probability of compound events is just like finding the theoretical probability of single events. We need to make a ratio for the number of favorable outcomes to the number of total outcomes.

​

P(compound event) = # of Favorable Outcomes

Total Number of Outcomes​

Subject | Subject

Some text here about the topic of discussion

​Imagine you have a spinner with 5 equal sides and you are flipping a coin. Make a table to show the sample space of this compound event, and give the probability your coin will land heads up and you will spin a 1, 2, 3 or 4.

Multiple Choice

You are spinning a 5 sided spinner and flipping a coin. What is the probability your coin will land on tails and you will spin a number greater than 3?

• 1/10

• 2/5

• 2/10

• 1/5

​You are flipping 3 fair coins. Write the sample space for all of the outcomes of this compound event and find the probability that at least two coins will land on heads.

Multiple Choice

You are flipping 3 fair coins. What is the probability that all of the coins will land on the same side?

• 1/8

• 2/8

• 1/4

• 1/2

​Each week, a clothing store gives away a shirt. The shirts vary by sleeve type (Long, Short, No Sleeve) and color (Grey, Blue, Pink). Draw a tree diagram to represent the sample space. What is the probability that the free shirt will have either long or short sleeves and be either pink or blue?

Multiple Choice

Using the same scenario from the previous problem, what is the probability you will get a short sleeve shirt that is grey or pink?

• 2/9

• 1/9

• 2/3

• 1/3

Fundamental Counting Principle
if an event or decision has a possible outcomes or choices, and another event has b possible outcomes or choices, then the total number of possible unique combinations of outcomes between the two is a⋅b.

​An ice cream shop offers bowls or cones and has 5 flavors

2 choices x 5 choices = 10 possible combinations

Multiple Choice

An ice cream shop offers a choice of three types of cones and 31 flavors of ice cream.  A customer gets to choose a cone and a type of ice cream.  How many different 1-scoop ice cream cones can a customer order? 

• 34
• 2
• 3
• 93

Multiple Choice

If you roll a die then flip a coin, how many possible outcomes?

• 2
• 6
• 12
• 64

Multiple Choice

How many outfits are possible with 5 pairs of jeans, 8 t-shirts, and 2 pairs of shoes?

• 15
• 40
• 80
• 10

Multiple Choice

Experimental Probability is:

• What Will happen 
• What actually happens
• What should happen
• What I think Happens

Multiple Choice

Theoretical Probability is?

• What Should happen
• What does happen
• What Will Happen
• What I want to Happen

Mutually Exclusive

Events that CANNOT occur at the same time

• A card deck has 4 suits (Diamonds, Hearts, Clubs and Spades)
  If picking only one card I cannot draw 2 suits

• A card deck has 12 numbers (Ace, 2, 3, 4, 5, 6, 7, 8, 9, 10, Jack, Queen, King)

  If picking only one card I cannot draw a 2 and an 8

Multiple Choice

If you are picking a card randomly from a deck of cards, the events of picking a jack and picking a heart are mutually exclusive.

• True

• False

Multiple Choice

If you are picking a card randomly from a deck of cards, the events of picking an ace and picking a ‘3’ are mutually exclusive.

• True

• False

Multiple Choice

When rolling a single die, the events of rolling an even number and rolling a ‘5’ are mutually exclusive.

• True

• False