A survey is conducted at a university involving 1,400 students. The students are either male or female and are also either domestic students or international students.

From the results of the survey, the following probabilities are found:

• probability that a random student is female is 0.51
• probability that a random student is an international student is 0.52
• probability that a random student is a female international student is 0.26
• probability that a random student is a female domestic student is 0.25
• probability that a random student is a male international student is 0.26
• probability that a random student is a male domestic student is 0.23

Let the events A and B be:

Event A: a random student is female

Event B: a random student is an international student

a)An incomplete tree diagram for this scenario is presented below. Fill in the correctnumber of outcomesfor each part of the tree. Give your answers as whole numbers.

international _____

female ______ <

domestic _______

<

international _____

male ______ <

domestic _______

b)Find the probability that a random student from this group is not an international student given that they are female. Give your answer as a decimal to 3 decimal places.

P(not B given A) =

-2 of 3ID:MST.FET.P.CP.02.0020A

A large group of 110 people sit down at a function to a two-course meal. Each course has two options: guests can choose to have either Main A or Main B, and they can choose to have either Dessert A or Dessert B.

After the function, the chef notes that 33 chose Main A, while the remaining 77 chose Main B. And of the people that chose main A, 14 chose Dessert A and 19 chose Dessert B. Of the people that chose Main B, 30 chose Dessert A and 47 chose Dessert B.

a)A tree diagram describing this situation has been drawn up, and some probabilities have been filled in. Complete the tree diagram for this scenario by filling in the appropriateprobabilityfor each part of the tree. Give your answers as decimals to 2 decimal places.

Dessert A _____

main A .30 <

Dessert B _______

<

Dessert A _____

main B .70 <

Dessert B _______

b)Find the probability that a random person from this group selects Main A and Dessert B. Give your answer as a decimal to 2 decimal places.

P(Main A and Dessert B) =

c)Find the probability that a random person from this group selects Dessert B given that they selected Main A. Give your answer as a decimal to 2 decimal places.

P(Dessert B|Main A) =

-3 of 3ID:MST.FET.P.CP.03.0020A

For the random process of rolling two six-sided dice and recording the sum, let A and B be the events defined by:

A: the result is an odd number

B: the result is greater than 7

a)Calculate the probability of B given A. Give your answer as a decimal to 2 decimal places.

P(B|A) =

b)Calculate the probability of A given B. Give your answer as a decimal to 2 decimal places.

P(A|B) =

A test for a particular illness that affects 9% of the general population has the following properties:

• The test will show a positive in 95% of cases where the patient has the illness and a negative in 5% of such cases.
• The test will show a false positive in 6% of patients who do not have the illness and a negative result for 94% of patients who do not have the illness.

Note that a positive result means that the test indicates that the patient has the illness. A negative result means that the test indicates that the patient doesn't have the illness.

A patient has just been tested and shows a positive result. Assuming all other things being equal, and based on the above information, find the probability that the patient does not have the illness. Give your answer as a decimal to 2 decimal places.

Probability that patient does not have illness =_______

An administrator who works at a train station has to monitor the drinks vending machine. When the machine gets low on stock, a warning light appears and the administrator is meant to contact the drinks supplier to refill the machine. However, the light is not always accurate. In particular, it will occassionally come on even when the stock is not low. The administrator knows the following probabilities:

• On average the vending machine is low on stock on 3 out of every 100 days. That is, the probability of the vending machine being low on a random day is 0.03.
• The warning light is very accurate when it comes to positively reporting low stock. Specifically, if the stockislow, the probability that the warning light will come on is 1.
• However, the warning light also occasionally comes on even if the stock is not low - although this is rare. The probability that the light will come on during the day when the stockisn'tlow is 0.002.

The administrator notices that the light has just appeared on the machine.

Based on this information, calculate the probability that the stock is low in the machine given that the warning light has just come on. Give your answer as a decimal to 3 decimal places.

P(stock is low|warning light is on) =________

In the Legal Eagle law firm, 63% of the lawyers are male while 37% are female. Of the male lawyers, 37% are corporate lawyers. Of the female lawyers, 28% are corporate lawyers.

If a corporate lawyer is chosen at random, calculate the probability that they are male. Give your answer as a decimal to 2 decimal places.

Probability =________