Probability of Compound Events

Probability ~ Compound Events

Probability

• how likely an event is to occur

• written as a fraction or decimal

• from 0 - 1

Multiple Choice

Find the P(even)

• likely

• 1/4

• 22.2%

• 2

Compound Event

• made up of 2 or more simple events (such as rolling a die & flipping a coin

• can be independent or dependent

Multiple Select

The two types of compound events are

• Independent

• Probability

• Dependent

• Sample Space

• Unlikely

Independent Event

the probability of one event DOES NOT affect the probability of another event

ex. the results of flipping a coin does not affect the results of rolling a die

Dependent Event

the probability of one event DOES affect the probability of another event ex pulling a card from a deck of playing cards, not replacing it and then pulling another card.

THE key phrase to look for is WITHOUT REPLACEMENT

How to Tell if it's Independent or Dependent?

• With replacement -> Independent

• Without replacement -> dependent

Multiple Choice

Identify the type of event as independent or dependent:

Tommy will flip a coin and spin a spinner.

• Independent

• Dependent

Multiple Choice

Identify the type of event as independent or dependent:

picking a marble from a bag, keeping it, and then picking another marble

• independent

• dependent

Multiple Choice

Identify the type of event as independent or dependent:

picking a marble from a bag, replacing it, then picking another marble from the same bag

• independent

• dependent

To find the probability of compound events...

Multiply the probabilities of each event P(A) x P(B)

Multiple Choice

Probability of die landing on 4 and spinner landing on reddish/orange color?

• 1/6

• 1/4

• 1/24

A bag has 5 red marbles, 2 green marbles and 3 blue marbles. When you select a marble, you keep it. What is P(red, then green)?

Multiple Choice

Why is this a dependent event?

• because it's talking about 2 events

• because one event affects the other.

• because you don't replace the marble

• because you replace the marble

P(red, then green)

• P(red) 5/10

• P(green) 2/9 (we assume that we got the red that we wanted, so there is one less total, but still 2 that are green)

• P(red, then green) 1/2(2/9) = 2/18 = 1/9

Multiple Choice

A bag has 2 black and 3 red marbles. You reach into the bag, select a marble and do not replace it. What is P(red, then red)?

• 9/25

• 1/9

• 3/10

• 1/72

Multiple Choice

A bag has 2 black and 3 red marbles. You reach into the bag, select a marble and then replace it. What is P(red, then red)?

• 9/25

• 1/9

• 3/10

• 1/72

Poll

So how much do you really understand?

• I totally get it! 100%

• I'm still kind of confused... 50%

• I don't understand at all! Help me! 25%

• I understand most of it...75%