This presentation is the property of its rightful owner.
1 / 10

# EXAMPLE 4 PowerPoint PPT Presentation

Dice. When two six-sided dice are rolled, there are 36 possible outcomes, as shown. Find the probability of the given event. The sum is not 6. The sum is less than or equal to 9. EXAMPLE 4. Find probabilities of complements. P ( sum is not 6). = 1 – P ( sum is 6). 5. = 1 –. 36.

EXAMPLE 4

An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.

- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -

#### Presentation Transcript

Dice

When two six-sided dice are rolled, there are 36 possible outcomes, as shown. Find the probability of the given event.

The sum is not 6.

The sum is less than or equal to 9.

EXAMPLE 4

Find probabilities of complements

P(sum is not 6)

= 1 – P(sum is 6)

5

= 1 –

36

31

0.861

=

36

P(sum< 9)

= 1 – P(sum > 9)

6

36

= 1–

30

=

36

5

0.833

=

6

EXAMPLE 4

Find probabilities of complements

A restaurant gives a free fortune cookie to every guest. The restaurant claims there are 500 different messages hidden inside the fortune cookies. What is the probability that a group of 5 people receive at least 2 fortune cookies with the same message inside?

The number of ways to give messages to the 5 people is 5005. The number of ways to give different messages to the 5 people is 500499498 497496. So, the probability that at least 2 of the 5 people have the same message is:

EXAMPLE 5

Use a complement in real life

SOLUTION

P(at least2are the same)

= 1 – P(none are the same)

500499498 497496

= 1 –

5005

0.0199

EXAMPLE 5

Use a complement in real life

Find P( A ).

P(A) = 0.45

0.55

=

for Examples 4 and 5

GUIDED PRACTICE

Find P( A ).

1

3

P(A) =

4

4

=

for Examples 4 and 5

GUIDED PRACTICE

Find P( A ).

P(A) = 1

0

for Examples 4 and 5

GUIDED PRACTICE

Find P( A ).

P(A) = 0.03

0.97

for Examples 4 and 5

GUIDED PRACTICE

The probability increases to about 0.097.

What If? In Example 5, how does the answer change if there are only 100 different messages hidden inside the fortune cookies?

for Examples 4 and 5

GUIDED PRACTICE