Week 4 Worksheet Name: KEY 1.

Week 4 Worksheet

Name:

KEY

Round your answers to at least 4 decimal places, show your work, place your answer on the line provided.

1. A survey found that 25% of pet owners had their pets bathed professionally rather than do it themselves. If 5 pet owners are randomly selected, find the probability that at least 1 pet owner has their pets bathed professionally.

P(At least one) = 1 ? P(none) = 1 1 pn 1 1 0.255= 0.7626

0.7626

2. The old telephone company rule for area codes was: the first digit could not be 0 or 1, the second digit had to be 0 or 1, and the third digit could be anything. How many different area codes are possible, using that definition?

8 210 160 3. Shade in the Venn diagram that illustrates the set AC B.

A

160

AC B

4. Draw and shade a Venn Diagram for A (B C)

5. One card is randomly draw from a standard deck. What is the probability of drawing a red card or a king? P(Red King) P(Red) P(King) P(Red King) 26 4 2 28 0.5385 52 52 52 52

0.5385

6. The Basket Store had the following premade gift baskets containing the following combinations in stock.

Cookies Mugs Candy Total

Coffee 20

13

15

48

Tea

18

16

12

46

Total 38

29

27

94

a) Choose one basket at random. Find the probability that it contains tea, given that it contains mugs.

P(T| M) P(T M ) 16 0.5517 P(M ) 29

0.5517

b) Are the events Tea and Candy independent for this data? Explain why or why not, using probabilities to back up your answer.

Circle one: Yes No

No, the probability that a basket contains tea and candy does not equal the marginal probabilities multiplied together:

P(T

C)

12 94

0.1277

P(T)

P(C)

46 94

27 94

0.1406

c) Are the events Tea and Candy mutually exclusive for this data?

Circle one: Yes No

Explain why or why not, using probabilities to back up your answer.

No, since the intersection does not equal zero.

P(T C) 12 0.1277 0 94

or

There is an overlap where 12 baskets contain both tea and candy.

7. The typical combination lock uses 3 numbers between 0 and 49, and they must be selected in the correct order. What is the probability of opening the lock on the first guess?

There are 50 numbers between 0 and 49. A number can be used in the locker combination more than once, for example you could have the combo 12-40-12. There is only one correct combo that will open the lock.

1 1 0.000008 505050 125000

0.000008

8. How many ways can you order 6 trophies on a fireplace mantel? There are 6 trophies to choose from to go in the first spot. Once a trophy is put down, there are 5 trophies left for the second spot, etc. 6 5 4 3 2 1 720 720

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