Statistics Probability Sample Problems

1. At a certain canteen, Doris can choose merienda from three drinks (Coke, Pepsi, Gulaman) and four sandwiches from (bacon, chicken, tuna, egg). In how many ways.

Solution:

D = {Coke, Pepsi, Gulaman}
N(D) = 3
S = {Bacon, Chicken, Tuna, Egg}
N(S) = 4

N1 . N2 = 3 x 4 = 12 ways

2. Two dice are rowed, in how many ways can they fall? If 3 dice are rowed? and if 4 dice are rowed?

For two dice
N1 = 6
N2 = 6
N1.N2 = 6 x 6 = 36 ways

For three dice
N1 . N2 . N3
6 x 6 x 6 = 216 ways

For four dice
N1.N2.N3.N4
6 x 6 x 6 x 6 = 296 ways

3. Using the digits 1,2,3,4,5,6, How many two-digit can be formed if a) repetition is allowed b) repetition is not allowed. How many numbers do we have to choose from the given set, they are 6 numbers.

Solution:

a) Repetition is allowed
6 x 6 = 36 ways

b) Repetition is not allowed
6 x 5 = 30 ways

Statistics Probability: Definitions, Principles and Samples

Probability which connotes the “chance” or the “likelihood” that something will happen or occur is an interesting and fascinating area of mathematics.

Probability – the part of mathematics that deals with the questions “how likely” is called probability or the theory of probability.

Probability – is a measure of certainty, its scale is from 0 to 1. A probability of zero indicates that there is no chance at all that an event will happen or occur. A probability of one (1) indicates absolute certainty that an event will happen. Absolute certainly rarely happens in lifes.

1. Experiment

Activity that can be done repeatedly.

Examples:
1. Tossing a coin
2. Rolling a pie


2. Sample Space – set of all possible outcomes in an experiment(s)

Examples:
a.) S = {H,T} n(S) = 2
b.) S = {1,2,3,4,5,6} n(S_ = 6
c.) S = {Rod, Ed, Emer} n(S) = 3

3. Sample Point – an element in the sample space

Examples
a.) H is a sample point
T is a sample point

4. Event – is a subset of sample space

Example:
Getting an even number when you roll a die is an event

S = {1,2,3,4,5,6}
E = {2,4,6}
n (E) = 3

Counting Techniques

N1 . N2 . N3 . N4 …..Nn (where N = event)

Fundamental Principles

If one thing can be done independently in N1 different ways and if a second thing can be done independently in N2 different ways and so on. Then the total number of ways in which all the things may be done in the stated order is N1 . N2 . N3 . N4 ……….