1 Age Category Team 1820 21 25 2630 Above 30 JumpingHigh JH

1)

Age Category

Team

{18-20}

{21 – 25}

{26-30}

Above 30

JumpingHigh (JH)

6

10

11

8

SpeedySkies   (SS)

3

5

8

20

WinterFun   (WF)

18

10

11

6

Give the literal formula first (not with numbers) and then solve:

“What is the probability of being in the JumpingHigh team given that you belong to the “above 30” age category?”

Give the literal formula first (not with numbers) and then solve:

“What is the probability of being a WinterFun member in the {21-25} age category?”

Give the literal formula first (not with numbers) and then solve: “What is the probability of being in {18-20} or {21 -25} age category given that you are a member of SpeedySkies team?”

Give the literal formula first (not with numbers) and then solve:

“What is the probability of not being a member of Speedy Skies team”

Is there any relationship between being a member in {21-25} age category and belonging to a specific team? (relationship between age and team) Use the probabilities of given operation to decide and explain your answer.

PROBLEM 4: Tattoos and Marriage (25 points)

A study of tattoos on women and marriage found the following:

Tattoo (T)

No Tattoo (T’)

Married (M)

200

800

1000

Not Married (M’)

300

400

700

500

1200

1700

Compute these probabilities:   

(a) P (M and T)

(b) P (M)

(c) P (M/T)   

(d) P (M or T)

(e) Is there a relationship between marriage and having a tattoo? Explain.

PROBLEM 5 (15 points)

(a) What if the probability of being a gum chewer or living in the Northeast?

(b) Is there a relationship between region and gum chewing? Explain.

Northeast

South

West

Chews Gum

100

70

130

Does Not Chew Gum

300

230

70

Age Category Team	{18-20}	{21 – 25}	{26-30}	Above 30
JumpingHigh (JH)	6	10	11	8
SpeedySkies   (SS)	3	5	8	20
WinterFun   (WF)	18	10	11	6

Solution

Post multiple questions to get the remaining answers

1)

a) P(being in jumping high given that your age is above 30) = P(being in jumping high with age more than 30)/[P(people with age more than 30)]

=> 8/(8+20+6)

=> 8/34

=> 4/17 = 0.2352

b) Probability of being a winter fun member in (21-25) category

=> 10/(10+5+10)

=> 10/25 = 2/5 = 0.40

c) What is the probability of being in {18-20} or {21 -25} age category given that you are a member of SpeedySkies team?”

[P(speedy skies with age 18-20) + P(speedy skies with age 21-25)]/P[speedy skies]

=> (3+5)/(3+5+8+20)

=> 8/36

=> 2/9 = 0.22222222

d) Probabilty of not being a member of speedy skies team = (3+5+8+20)/(35+36+45)

=> 36/(116)

=> 0.3103

e) No, there is no relationship