**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,

**A total less than 10 using the definition of the compliment of an event.**

c)

c)

**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,

**A total less than 9 using the definition of the compliment of an event.**

c)

c)

**
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)