Question 1 A set of 106 hypothetical CWU students were surve

Question 1:

A set of 106 hypothetical CWU students were surveyed about whether they lived on or off campus and how much ice cream they ate per week. The results are shown below:

(a) What is the probability that a randomly chosen student lives on campus?

(b) If a person eats at most two scoops of ice cream per week, what is the probability that they live on campus?

(c) If a person lives on campus, what is the probability that they eat at most two scoops of ice cream per week?

(d) Are the events \"lives on campus\" and \"eats at most two scoops of ice cream per week\" independent? Your answer should be \"Y\" or \"N\".

Question 2:

Herbert has a bag of jelly beans that contains 9 black beans (ugh!) and 7 orange ones. He reaches in and draws out two, without replacement. Draw a probability tree and use it to answer the questions below:
(a) What is the probability he drew an orange bean on the second draw?

(b) What is the probability that at least one of his beans is orange?

Question 3:

Widgets at the Springfield Power Plant come from three different suppliers: 44% from Widgets-R-Us, 45% from Burns Widgetworks, and 11% from Shelbyville Sprockets. Experience shows that 15% of the widgets from Widgets-R-Us are defective, as are 8% from Burns Widgetworks and 70% from Shelbyville Sprockets. Homer chooses a widget from the supply room at random. Draw a probability tree for this problem, and use it to answer the questions below.
(a) What is the probability Homer chose a defective widget?

(b) What is the probability that Homer chose a non-defective widget or one from Burns Widgetworks?

(c) Are the events \"defective widget\" and \"widget from Shelbyville Sprockets\" independent? Your answer should be \"Y\" or \"N\".

Question 4:

An unbalanced coin shows heads 55% of the time.
(a) If the coin is tossed 10 times, what is the probability of heads on all tosses?

(b) Find the probability of at least one head in 10 tosses.

Question 5:

About 1.7% of the population will have a particular type of cancer. The test for this particular type of cancer is 96.4% accurate, that is, 96.4% of those with the cancer test positive, while 96.4% of those without the cancer test negative. Given that someone has received a positive test, what is the probability they have cancer?
(a) Given that someone has received a positive test, what is the probability they have cancer?

(b) Given that someone has received a negative test, what is the probability they do not have cancer?

Question 6:

Are the following random variables discrete or continuous? Your answer should be either \"discrete\" or \"continuous\".
(a) The number of texts you receive in a day.

(b) The length of the walk from this class to your next one.

(c) Your shoe size.

Question 7:

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Question 12:

Question 13:

Bill and Fred are betting on the outcome when two fair dice are rolled. If the dice sum is any even number, other than 8, Bill pays Fred $5. If the dice sum is 8, Bill pays Fred $2. If the dice sum is odd, Fred pays Bill $2. What is Fred\'s expected payoff for this game?

Question 14:

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Question 16:

Solution

a) the probability that a randomly chosen student lives on campus = 59/106 =0.5567

b) a person eats at most two scoops of ice cream per week, the probability that they live on campus =28/48 = 0.5833

c) If a person lives on campus, the probability that they eat at most two scoops of ice cream per week=28/59 = 0.4746

d) No

For 300 points one question with 4 subdivisions answered.