PROBLEM 3 (15 points): Gift Baskets The Gift Basket Store had the following prem
ID: 3125193 • Letter: P
Question
PROBLEM 3 (15 points): Gift Baskets
The Gift Basket Store had the following premade gift baskets containing the following combinations in stock:
Cookies
Mugs
Candy
Coffee
20
13
10
Tea
12
10
12
Choose one basket at random. Find the probability that it contains
Coffee or candy
Tea given that it contains mugs
Tea and cookies
PROBLEM 4 (15 points): Olympic Medals
The medal distribution from the 2004 Summer Olympics games for the top 23 countries is shown below:
Gold Silver Bronze
United States 35 39 29
Russia 27 27 38
China 32 17 14
Australia 17 16 16
Others 133 136 153
a) Find the probability that the winner won the gold medal, given that the winner was from the United States.
b) Find the probability that the winner was from the United States, given that she or he won a gold medal.
c) Are the events “medal winner is from United States” and “gold medal won” independent? Explain
PROBLEM 5 (10 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?
Northeast
South
West
Chews Gum
100
230
130
Does Not Chew Gum
300
80
70
PROBLEM 6 (35 points): given in a previous midterm
Some collected data is presented in the table below:
Age
Team
{18-20}
{21 – 25}
{26-30}
Above 30
Jumping High
6
10
11
8
35
Speedy Skies
3
5
8
20
36
Winter Fun
18
10
11
6
45
27
25
30
34
116
Give the literal formula first (not with numbers) and then solve:
“What is the probability of being in the highest age category given that you are a Winter Fun member”
Give the literal formula first (not with numbers) and then solve:
“What is the probability of being a Speedy Skies member of 29 years old”
Give the literal formula first (not with numbers) and then solve: “What is the probability of being younger than 26 years given that you are a member of Jumping High 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 in {18-20} age category and belonging to a specific team? (relationship between age and team)
Cookies
Mugs
Candy
Coffee
20
13
10
Tea
12
10
12
Explanation / Answer
Problem 3:
P(Coeffee or Candy) = P(Coeffee) + P(Candy) - P(Coeffee and Candy) = 43/77 + (22/77) - (10/77) = 0.7143
P(Tea / it contain mugs) = P(Tea and It contain mugs) / P(mugs) = (10/77) / (23/77) = 0.4348
P(Tea and Cookies) = 12/77 = 0.1558
Problem 4:
The probability ( gold medal/United States.) = P(Gold medal and US) / P(US) = 35/729 / 103/729 = 0.3398
The probability(United States/ gold medal) = P(US and Gold Medal) / P(gold medal) = 35/729 / 244/729 = 0.143
A and B are independent if P(A and B ) = P(A).P(B)
Here, P(US) P(gold medal)= (103/729)((244/729) = 0.04729
P(US and gold medal) = 0.0480
Therefore, they are not independent
Problem 5:
Probability of being a gum chewer or living in the Northeast= P(Chewer gum) + P(Northeast) - P(Chewer gum and Northeast) = (460/910) + (400/910) - (100/910) = 0.835
More percentage of Northeast persons not used chewers gum,
More percentage of South persons used chewers gum
on general, average percentageof west persons used chewers gum
Question 6:
The probability of being in the highest age category given that you are a Winter Fun member is
= P(Hieghest age category and Winter Fun) / P(Winter Fun) = P(34/116) / (45/116) = 0.293
The probability of being a Speedy Skies member of 29 years old = P(Speedy skies and 29 years old) = 8/116 = 0.0689
The probability of being younger than 26 years given that you are a member of Jumping High team is
P(Yourng than 26 years and jumping HIgh) / P(jumping High team) = 19/116 / 35/116 = 0.5428
The probability of not being a member of Speedy Skies team is 1 - P(speedy skies) = 1 - 36/116 = 0.6896
P(age 18-20) P(Jumping high) = (27/116)*(35/116) = 0.07022 not equal to P(age 18-20 and jumping high) = 6/116 = 0.05172. Therefore age 18-20 and jumping high not independent
P(age 18-20) P(speed skills) = (27/116)*(36/116) = 0.0722 not equal to P(age 18-20 and speed skills) = 3/116 = 0.02586. Therefore age 18-20 and speed skills not independent
P(age 18-20) P(winter fun) = (27/116)*(45/116) = 0.09029 not equal to P(age 18-20 and winter fun) = 18/116 = 0.155. Therefore age 18-20 and winter fun not independent
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