Addition Rule of Probability
It simply refers to the likelihood of an event taking place whenever the occurrence of an event is uncertain. The probability of a single event can be calculated by dividing the number of successful trials of that event by the total number of trials.
Expected Value
When a large number of trials are performed for any random variable ‘X’, the predicted result is most likely the mean of all the outcomes for the random variable and it is known as expected value also known as expectation. The expected value, also known as the expectation, is denoted by: E(X).
Probability Distributions
Understanding probability is necessary to know the probability distributions. In statistics, probability is how the uncertainty of an event is measured. This event can be anything. The most common examples include tossing a coin, rolling a die, or choosing a card. Each of these events has multiple possibilities. Every such possibility is measured with the help of probability. To be more precise, the probability is used for calculating the occurrence of events that may or may not happen. Probability does not give sure results. Unless the probability of any event is 1, the different outcomes may or may not happen in real life, regardless of how less or how more their probability is.
Basic Probability
The simple definition of probability it is a chance of the occurrence of an event. It is defined in numerical form and the probability value is between 0 to 1. The probability value 0 indicates that there is no chance of that event occurring and the probability value 1 indicates that the event will occur. Sum of the probability value must be 1. The probability value is never a negative number. If it happens, then recheck the calculation.
- In a survey conducted by Helena, a financial consultant, it was revealed of her 412 clients
281 own stocks.How many of Helena's clients own stocks, bonds, and mutual funds? (Assume each client invested in at least one of the three types of funds.)
190 own bonds.
181 own mutual funds.
117 own both stocks and bonds.
106 own both stocks and mutual funds.
103 own both bonds and mutual funds.
clients - In an election being held by the Associated Students Organization, there are seven candidates for president, five for vice-president, four for secretary, and six for treasurer. How many different possible outcomes are there for this election?
outcomes - There are ten seniors and six juniors in the Math Club at Jefferson High School. In how many ways can a math team consisting of four seniors and three juniors be selected from members of the Math Club?
ways - From a shipment of 75 transistors, 6 of which are defective, a sample of 4 transistors is selected at random.
(a) In how many different ways can the sample be selected?
ways
(b) How many samples contain exactly 3 defective transistors?
samples
(c) How many samples do not contain any defective transistors?
samples - A sample of 3 balls is to be selected at random from an urn containing 20 balls numbered 1 to 20. Five balls are green, 6 balls are white, and 9 balls are black.
(a) How many different samples can be selected?
samples
(b) How many samples can be selected that contain at least 1 white ball?
samples
- Let
U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10},A = {1, 3, 5, 7, 9},B = {2, 4, 6, 8, 10},andC = {1, 4, 6, 7, 8, 9}.List the elements of each set. (Enter your answers using roster notation. Enter EMPTY or ∅ for the empty set.)
-
Write the set in set-builder notation.{4, 5, 6, 7, 8}{x | x = ,where n is an integer between 4 and inclusive
Check the boxes in the accompanying figures to indicate which regions should be shaded to represent each set. (Select all that apply.)
- Let U denote the set of all employees in a hospital, and let
| N | = | {x U | x is a nurse} |
| D | = | {x U | x is a doctor} |
| A | = | {x U | x is an administrator} |
| M | = | {x U | x is a male} |
| F | = | {x U | x is a female}. |
Describe each set in words.
- Refer to the following Venn diagram, and list the points that belong to each set. (Enter your answer using roster notation. Enter ∅ for the empty set.)
- AC ∩ BC ∩ CC
- List the elements of the set in roster notation. (Enter EMPTY or ∅ for the empty set.)
{x | x is a letter in the word HIPPOPOTAMUS}
- Determine whether the pairs of sets are disjoint.
- List the elements of the set in roster notation. (Enter EMPTY or ∅ for the empty set.)
Let
and
- List the elements of each set. (Enter your answers using roster notation. Enter EMPTY or ∅ for the empty set.)
(b) (A ∪ B ∪ C)c
(c) (A ∩ B ∩ C)c
- Let U denote the set of all students who applied for admission to the freshman class at Faber College for the upcoming academic year and let
A = {x U | x is a successful applicant}
B = {x U | x is a female student who is enrolled in the freshman class}
C = {x U | x is a male student who is enrolled in the freshman class}(a) Use Venn diagrams to represent the sets U, A, B, and C. (Label the answer blanks with the correct letters.)C - A ∩ B ∩ CC
AC ∩ B ∩ C
Find the smallest possible set (i.e., the set with the least number of elements) that contains the given sets as subsets. (Enter your answer using roster notation. Enter EMPTY or ∅ for the empty set.)
- List the elements of the set in roster notation. (Enter EMPTY or ∅ for the empty set.)
{x | x is a letter of the word TALLAHASSEE}
- Let A and B be subsets of a universal set U and suppose n(U) = 370, n(A) = 150, n(B) = 80, and n(A ∩ B) = 50. Find the number of elements in the set.
n(Ac)elements
- Let A and B be subsets of a universal set U and suppose n(U) = 380, n(A) = 150, n(B) = 90, and n(A ∩ B) = 40.
n(Ac ∩ B)elements
- = 390, n(A) = 140, n(B) = 90, and n(A ∩ B) = 40.
n(Ac ∩ Bc)
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