Probability of getting exactly two heads

 

 

 

 

 

Question 1
Assume you toss a coin 2 times. Draw a tree diagram and write the sample space. Calculate the following probabilities.

a) Probability of getting exactly two heads

b) Probability of getting at least one head

Question 2
In a survey of high school students, 18 preferred engineering, 29 preferred math and 13 preferred science as their primary career choice. If a student is selected at random, find the probability that:
a) The student preferred math:

b) The student preferred engineering or science:

Question 3 ____
a) A shop offers 8 types of jackets, 6 types of trousers and 5 types of silk ties. If a shopper selects one jacket, one set of trousers and one silk tie, how many outcomes are possible?

b) The facilities manager of a company wants to choose 3 candidates from 7 to assign different tasks. Thus, the order is important. How many ways can the manager arrange them?

 

 

Question 4
At a large company, the employees were surveyed and classified according to the educational level and whether they attend a sports event at least once a month. The data are shown in the table.

Sports event Educational Level
High School Undergraduate Graduate
Attend 14 18 16
Do Not Attend 12 19 21

If any employee is selected at random, find the probability that the person:
i) Has undergraduate education:

ii) Attends sports event and has high school education:

iii) Has graduate education or do not attend sports event:

iv) Has graduate education given the person attends sports events:

Question 5
The probability that a person owns a car is 0.80.The probability that a person owns a boat is 0.3 and that the person owns both car and the boat is 0.12. Find the probability that the person owns either the car or the boat?

 

 

Question 6 [3 Marks]
In a survey 38% participants said, they feel stressed at the work place. If a sample of 25 such persons are selected, find:
a) The probability that exactly 9 say that they are stressed at the work place.

 

b) The mean and variance for the sample.

 

 

 

 

 

 

 

 

 

Probability
Classical probability rule for a simple event:
Classical probability rule for a compound event:
Conditional probability of an event:

Multiplication rule for dependent events:

Multiplication rule for independent events:

Addition rule for mutually nonexclusive events:

Addition rule for mutually exclusive events:

Factorial :

Combination Rule:

Permutation rule:

Binomial probability Distribution

Binomial probability formula:

Mean and standard deviation of the binomial distribution: