Probabilty Knowledge Examples

 

Lets assume that the student asked the solutions to the below questions.

 

Questions

 

1.      Two fair dice are thrown. What is the probability of getting two sixes? Draw a probability tree and table and confirm your answer.

 

2.    A red and white die are thrown simultaneously. Find the probability of the following events:

a) A total of 6 and the larger number on the blue die,
b) Both dice show 3,
c) A total less than 10 using the definition of the compliment of an event.

3.    Expand

 

4.      If the probability of a marksman hitting a bullseye is 0.9, what is the probability of the marksman hitting 7 bullseye in eight shots?

   

 

Questions which will help you to solve your questions.

 

Question 1: If a fair coin and a die is tossed what is the probability of getting head and four? Draw a probability tree and table and confirm your answer

 

Answer: If a fair coin and a die is tossed, the probability of getting head and four is  and  respectively. Hence,

 

p(head and four)

 

Probability tree

 

From the probability tree, there are 12 outcomes. The probability of getting head and four is one out of 12 possible outcomes.

 

 

Again from the probability table, there are 12 outcomes. The probability of getting head and four is one out of 12 possible outcomes.

 

Question 2: A red and black die are thrown simultaneously. Find the probability of the following events:

a) A total of less than 5 or greater than 10,
b) None of the dice show 3,
c) A total less than 9 using the definition of the compliment of an event.

 

Answer:

a) A total of less than 5 and greater than 10 are 2, 3, 4, 11 and 12. They require:

 

Total 2: R1, B1 or

Total 3: R1, B2 or R2, B1 or

Total 4: R1, B3 or R2, B2 or R3, B1 or

Total 11: R5, B6 or R6, B5 or

Total 12: R6, B6

 

And

p(Total 2)

p(Total 3)

p(Total 4)

p(Total 11)

p(Total 12)

p(Total less than 5 of greater than 10)

 

It is easy to answer probability questions if you go about it systematically. If in doubt use the probability table.

 

p(Total less than 5 of greater than 10)

 

 

Question 3: Expand

Answer: The Binomial expansion is

In this question ,  and  Hence

 

    

                                                       

                                                     

 

Question 4: If the probability of a student answering a question correctly in an exam is 70%, what is the probability that he will answer seven questions in an exam paper containing 10 questions?

 

Answer:  ,  

 

p(7 correct answers)