1) Age Category Team {18-20} {21 – 2 5} {26-30} Above 30 JumpingHigh (JH) 6 10 1
ID: 3403417 • Letter: 1
Question
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
Explanation / Answer
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
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