Probability of Dependent Events

Probability of Dependent Events

Math II Honors

Mr. Coleman

Unit 6 - Probability

Lesson Objectives

• Distinguish dependent events from independent events

• Define and compute conditional probabilities

• Compute probabilities from two-way tables

• Apply conditional probability for problem solving

Dependent Events

• Outcome of one event directly affects outcome of another event

• On 1st draw - 2/5 chance of pulling blue

• After the first draw, the probability of a second blue marble changes if we don't replace the first one

• This means these are dependent events.

Multiple Choice

Pablo chooses a colored marble from a mixed bag and writes down the color. Pablo leaves it out and then draws another.

• Independent

• Dependent

Multiple Choice

Clara picks a marble at random, puts it back, and then picks another marble at random.

• independent

• dependent

Conditional Probabilities

• Determines the probability of an event occuring given that another event has already happened.

• Math notation: P(A|B)

• Means: "Probability of A, given B"

• Only relevant for dependent events

• P(A|B) = P(A and B)/P(B) 

Multiple Choice

A new credit card has been issued to 2000 customers. Of these customers, 1500 hold a Visa, 500 hold an AA card, and 40 hold a Visa and AA card. Find the probability that a random chosen customer holds an AA, given they hold a Visa.

• .0267

• 37.5

• .02

• .3333

Probabilities from Two-Way Tables

When reading a two-way table to compute probabilities, the key is to identify the values that are pertinent to the problem.

ex: P(male AND sportscar) = 39/240

ex2: P(male | sportscar) = 39/84

Multiple Choice

What is the chance a randomly selected surveyed person drives an SUV? (Reduce your fractions!)

• 7/20

• 13/15

• 7/15

• 13/20

Multiple Choice

Suppose a randomly selected survey respondent was found to be a female respondent. What is the chance they are an SUV driver, given that they are female? (Reduce fractions!)

• 45/52

• 9/16

• 3/4

• 13/15

Exit Ticket

Answer the following questions to check your understanding from this lesson!

Multiple Choice

Is the event INDEPENDENT or DEPENDENT?
Amy plays card games.  She picks a card at random.  Then without putting the first card back, he picks a second card at random.

• Independent
• Dependent

Multiple Choice

Find the probability if you pick a card, do not replace it, then pick another card.

p(black, then white)

• 15/56

• 5/14

• 3/28

Multiple Choice

Consider the following table with information about all of the students taking Statistics at Happy High School.

Find P( Female | Part-time) =

• 15/31

• 43/71

• 31/43

• 15/43