Two-Way TablesGeneral Addition Rule

Aim: Create & use two-way tables to find probabilities involving ‘or’.

Try this …

Suppose in 2010, the Tampa Bay Rays ran a promotion at home games where each fan won a free taco if the team scored 7 or more runs.

1. What is the probability that a fan got a taco?

2. What is the probability that the Rays won?

Aim: Create & use two-way tables to find probabilities involving ‘or’.

≈ 18.5%

≈ 60.5%

And

What is the probability that a fan got a taco and was at a winning game?

≈ 16.0%

Aim: Create & use two-way tables to find probabilities involving ‘or’.

General Addition Rule (Or)

If we want to know the probability that a fan got a taco or was at a winning game:

We’ll be overlapping the probability of getting a taco and being at a winning game.

P(taco or win) = P(taco) + P(win)

- P(taco and win)

≈ 16%

Aim: Create & use two-way tables to find probabilities involving ‘or’.

Mutually Exclusive

In the past, the events had nothing to do with eachother (mutually exclusive):

P(Ace and King) =0%

P(Ace or King) =

≈ 15%

Aim: Create & use two-way tables to find probabilities involving ‘or’.

Now we are considering events that overlap:

P(Heart and King) =P(Heart or King) =

≈ 31%

Aim: Create & use two-way tables to find probabilities involving ‘or’.

PracticeDuring the last round of golf, Randy used his driver 15 times. For each of these 15 drives, he recorded whether or not the ball traveled at least 250 yards and whether or not the ball landed in the fairway. The results are shown in the table.

a. Create a two-way table to summarize the results of Randy’s drives.

b. What is the probability that Randy’s drive went over 250 yards or landed on the fairway?

≈ 86.7%

Aim: Create & use two-way tables to find probabilities involving ‘or’.