Conditional Probability: Independent & Dependent Events

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Conditional Probability

Learning Objective: Find probability given

Independent and Dependent Events

Conditional Probability

The probability of event B occurring knowing event A already occured

Real world example

A die is rolled. What is the probability of landing on a 5 if you

already know it lands on an odd number?

Reduced Sample Space

1, 2, 3, 4, 5, 6

The total Sample
Space is 6 but we
only care about
odd Numbers

Independent Events

What happens in one event does not change the probability of the
other event happening (Second outcome is not affected by the first
event). Key Word: “with replacement”

For Example: Tossing a coin, rolling dice, picking a card from a deck
with replacement.

Independent Events

Example 1: Landing on Heads after
tossing a coin and rolling a 5 on a
single 6-sided dice.

Example 2: Choosing a 3 from a
deck of cards, replacing it, and then
choosing an ace as the 2nd.

P (A and B) = P(A) ×P(B)

What happens when you toss
the coin does not affect what
happens when you roll the dice.

Event A does not affect Event B
because you replaced the card.

Dependent Events

What happens in the first event affects the outcome of the 2nd event. Key

word “without replacement”

Example 1: Robbing a bank and going to jail.

Example 2: Picking a card from a deck without
replacement. Then, picking another card from the
deck.

PA and B=PA ×P(B given A)

Multiple Choice

If you draw out a red marble, keep it, then draw out a blue marble, is it independent or dependent probability?

• Independent

• Dependent

Multiple Choice

If you Flip a coin two times, is it independent or dependent?

• Independent

• Dependent

Multiple Choice

If you Flip a coin then roll a 6-sided dice. Is it dependent or Independent?

• Independent

• Dependent

Multiple Choice

Dependent probability happens when the first item is not replaced, causing the total outcome to decrease by 1.

• True

• False

Multiple Choice

Independent Probability happens when the probability of the first event does not affect the probability of the second event.

• True

• False

See Lesson Video

Students do the next two examples.

Independent Practice/Homework (All Problems)

1.)A cooler contains 13 bottles of sports drink:
Five lemon-lime flavored, five orange flavored,
and three fruit punch flavored. You randomly
grab a bottle. Then you return the bottle to
the cooler, mix up the bottles and randomly
select another bottle. Both times you get a
lemon-lime drink.

Dependent or Independent

2.) Your Sock drawer has four white socks, two
brown socks, and two black socks. You randomly
pick two socks and get a matching pair of black
socks.

Dependent or Independent

​​Go to next slides so students can enter their response and Play lesson video

Math Response

Enter your answer as an unreduced fraction

Type answer here

Correct Answer: \frac{25}{169}

Deg^°

Rad

Math Response

Enter your answer as an unreduced fraction

Type answer here

Correct Answer: \frac{1}{28}

Deg^°

Rad

Play lesson video to go over questions.

Poll

On a scale from one to 5, how did you feel about today's lesson?

• 1

  I need help. I need to go to tutoring.

• 2

  I have questions but don't need tutoring. I understood a little.

• 3

  somewhere in between need practice and have questions.

• 4

  Feeling okay just need practice.

• 5

  I got this