Math AA SL: Probability

#MAASL00146

[Maximum Mark: 9]

There is a class of  students,  own a book and  own a tablet, and  own neither.

The variables shown below represent the students.

a)

i) Find .

ii) Find .

iii )Find  and .

b)
i) What is the probability that a student owns a tablet?

ii) What is the probability that a student owns a tablet or a book but not both?

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#MAASL00173

[Maximum Mark: 6]
There are 2 events  and 

 and 

a) Determine 

b) It is given that  Find 

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#MAASL00174

[Maximum Mark: 6]

There are 2 events  and 

 and 

a) Determine 

b) It is given that  Find 

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#MAASL00145

Consider events  and , where , , and 



a) Write down the values for , , and 

b) Solve for the value of 

c) Therefore, or otherwise, demonstrate that events  and  are not independent 

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At Rockford High School, students are required to take either Chemistry or Physics. 
It is known that  percent of the students take Chemistry and 55 percent take Physics.

a) Find the percentage of students who take both Chemistry and Physics

b) Find the percentage of students who take Chemistry, but not Physics
 
At Rockford High School,  percent of the students are girls, and  percent of
the girls take Chemistry. 
 
A student is chosen at random. Let  be the event that the student is a girl.
Let  be the event that the student takes Chemistry.
 
c) Find 
 
d) Show that  and  are not independent
 
A boy is chosen at random. 
 
e) Find the probability he takes Chemistry

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#MAASL00155

[Maximum Mark: 6]

A bag contains twelve orange marbles and four blue marbles. 
Gary selects a marble from the box. He replaces the marble and grabs a second one.

a) What is the probability that the first marble chosen is orange?

b) What is the probability that gary chooses 2 orange marbles?

c) What is the probability that one marble is orange and the other is blue?

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#MAASL00070

[Maximum Mark: 8]

A biased four-sided die is rolled, with the probabilities of each score 
shown in the table provided below. 

a) Find the value of x.

b) Find the expected value of the score.

c) The die is rolled 69 times. On how many occasions should one expect to obtain a score of 4?

                                             

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#MAASL00153

[Maximum Mark: 6]

A four sided dice is rolled, and the results are shown below


a) Find the value of k.

b) Find the expected value of the score.

c) The die is rolled 10 times. On how many occasions should one expect to obtain a score of 3?

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#MAASL00154

[Maximum Mark: 6]

A four sided dice is rolled, and the results are shown below


a) Find the value of k.

b) Find the expected value of the score.

c) The die is rolled 1,000 times. On how many occasions should one expect to obtain a score of 1?

Detailed Answer/Video Explanations Answer

#MAASL00207

[Maximum Mark: 7]

A biased six-sided die is rolled, with the probabilities of each score 
shown in the table provided below. 

a) Find the value of x.

b) Find the expected value of the score.

c) The die is rolled 43 times. On how many occasions should one expect to obtain a score of 3?

               

Detailed Answer/Video Explanations Answer

#MAASL00208

[Maximum Mark: 7]

A biased five-sector spinner is tested, with the probabilities of each score 
shown in the table provided below. 

a) Find the value of x.

b) Find the expected value of the score.

c) The spinner is tested 92 times. On how many occasions should one expect to obtain a score of 5?

                      

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