1) In a recent survey of college freshman, 42% of students checked the box next to “exercise regularly”, 45% checked the box next to “eat five or more servings of fruits and vegetables a day”, and 21% checked the box “neither.” Use the appropriate probability notation in your answers to each question.

First, put student responses in the appropriate boxes of our two-way relative frequency table:

Exercise (E)

̅

𝐸 Totals

100%

Eats fruit and veggies (Fv)

̅̅̅̅ 𝐹𝑣

Totals

Use the appropriate probability notation in your answers to each question.

a) What is the joint probability of randomly selecting a surveyed freshman who exercises and eats 5 servings of fruits and vegetables each day?

b) What is the probability of selecting a freshman who exercises regularly or eats 5 servings of fruits and vegetables each day?

c) What is the probability of a student not eating fruits or vegetables?

d) What is the probability of a freshman not exercising regularly and not eating 5 servings of fruits and vegetables each day?

e) Complete this conditional relative frequency table rounding to the whole nearest percentage (e.g. 12%).

̅ Exercise (E) 𝐸

̅̅̅̅ 𝐹𝑣

f) Is there an association between eating fruits and vegetables and exercise? Explain fully.

2)  In Canada 92% of households have televisions (T).  72% of households have televisions and internet (I) access.  5% have neither.  

a)  Complete the two- way relative frequency table:

I

Total

T

Total

100%

Use the appropriate probability notation in your answers to each question.

b)  What is the probability of selecting a Canadian house at random that has internet access but no television?

c)  What is the conditional probability of selecting a house that has internet given that it has a television?

d)  Of the house that do not have televisions, what is the conditional probability of selecting one that has internet access?

e)  Complete this conditional relative frequency table rounding to the whole nearest percentage (e.g. 12%).

Checked bag yes

Checked bag no

Business traveler yes

Business traveler no

f)  Is there an association between television ownership and internet access is Canadian homes?

A standard deck of playing cards contains 52 cards.One card is selected from the deck.

(a) Compute the probability of randomly selecting a club or spade?

(b) Compute the probability of randomly selecting a club, spade or heart?

(c) Compute the probability of randomly selecting a three or spade?

Suppose three students are selected at random. Let A be the random 
variable representing the number of ABM students that are selected.

16. What is the probability that there will be no ABM student selected?
A. 8/27      B. 4/9      C. 19/27      D. 1

17. What is the probability that at most 2 ABM students are selected? (2 points)
A. 0      B. 0.2222      C. 0.4444      D. 0.9630

18. What is the probability that less than 2 ABM students are selected? (2 points)
A. 0.2222      B. 0.7407      C. 0.9630      D. 1

19. What is the mean of the probability distribution of the random variable A? (2 
points)
A. 0.5      B. 0.67      C. 1      D. 1.3

20. What is the variance of the probability distribution of the random variable A? (2 
points)
A. 0      B. 0.33      C. 0.44      D. 0.66