Mutually Exclusive Events

Ex 1 Baseball pitchesMarie, at bat for the Coyotes, wants to hit a

fastball or a slider.

Anton throws the following

Curveball. P(C) = 1/3

Slider. P(S) = 1/2

Fastball. P(F) = 1/6

Find the probability that Marie gets a pitch she wants

P(F or S) = 1/6 + 1/2 = 4/6 = 2/3

The possible events in this question are said to be mutually

exclusive since they can not occur at the same time.

P(A or B) = P(A) + P(B)

Ex. If two dice are rolled, find the probability that

a) A total of 2 or 12 will occur

A: rolling a 2

B: rolling a 12

P(A) = 136

P(B) = 136

P(A or B) = P(A) + P(B)

Because they are mutually exclusive…

= 136

+ 136

= 236

= 118

b) 4 or a pair will occur

A: total of 4

B: pair

1 2 3 4 5 6

1 2 3 4 5 6 7

2 3 4 5 6 7 8

3 4 5 6 7 8 9

4 5 6 7 8 9 10

5 6 7 8 9 10 11

6 7 8 9 10 11 12

n(A) = P(A) = 3 / 363

1 2 3 4 5 6

1 2 3 4 5 6 7

2 3 4 5 6 7 8

3 4 5 6 7 8 9

4 5 6 7 8 9 10

5 6 7 8 9 10 11

6 7 8 9 10 11 12

n(B) = P(B) = 6 / 366

1 2 3 4 5 6

1 2 3 4 5 6 7

2 3 4 5 6 7 8

3 4 5 6 7 8 9

4 5 6 7 8 9 10

5 6 7 8 9 10 11

6 7 8 9 10 11 12

P(A or B) = + 6/363/36 -1/36 = 2/9

1 2 3 4 5 6

1 2 3 4 5 6 7

2 3 4 5 6 7 8

3 4 5 6 7 8 9

4 5 6 7 8 9 10

5 6 7 8 9 10 11

6 7 8 9 10 11 12

P(A or B) = + P(B)P(A) - P(A and B)

For Non-Mutually Exclusive events

P(A U B) = P(A) + P(B) – P(A B)

U

Homework

• Pg 340 1 together

• 3, 4a, 5, 6,7

• Test?

If A and B have no outcomes in common, they are said to be mutually exclusive events:

P(A U B) = P(A) + P(B)