# Using conditional probability and independence to interpret data

## Use data presented in two-way frequency tables to approximate conditional probabilities and to decide if events are independent (S-CP.A.4).

Students continue their work with two-way tables, using them to approximate conditional probabilities by using the tables as a sample space, and extending their work to consider independence.

1 The Titanic 2

WHAT: This is the second Titanic task in the series of three. Students examine the table from "The Titanic 1" to answer questions such as “Are the events ‘passenger survived’ and 'passenger was first class’ independent events?”

2 Rain and Lightning.

WHAT: In this short four-part task, students are given probabilities for rain, lightning, both, or (in part b) one conditioned on the other. Students are asked to determine whether rain and lightning are independent events, and the probabilities of various outcomes.

WHY: Part a uses the meaning of independence. Part b uses conditional probability of A given B as P(A and B)/P(B). Parts c and d use the Addition Rule outside of a uniform probability model.

## External Resources

1 Three Shots

#### Description

WHAT: The teacher’s guide gives this description: “In the 2005 Conference-USA Tournament game, Memphis player Darius Washington Jr. was fouled at the buzzer during a three-point shot. With his team down by two to Louisville, he stepped up to the foul line for three shots. In this lesson, students will compute the probabilities of a win, loss, or tie for Memphis. They will also determine whether or not it was smart for Louisville to foul at the buzzer, and will investigate the conditions when fouling at the buzzer in a close game makes sense.”

WHY: Three Shots is an application of many of the ideas in this unit, including conditional probability and independence (S-CP.A.5, S-CP.B.6) and calculating the probabilities of compound events.

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