$P\left(A\right)=0.59$
$P\left(B\right)=0.46$
$P\left(A\cap B\right)=0.28$
 $find\ \ P\left(A\cup B\right).$ 

$P\left(A\right)=0.59$
$P\left(B\right)=0.46$
$P\left(A\cap B\right)=0.28$
 $find\ \ P\left(A\cap\overline{B}\right).$ 

$P\left(A\right)=0.59$
$P\left(B\right)=0.46$
$P\left(A\cap B\right)=0.28$
 $find\ \ P\left(\overline{A}\cap\overline{B}\right).$ 

$P\left(A\right)=0.59$
$P\left(B\right)=0.46$
$P\left(A\cap B\right)=0.28$
 $find\ \ P\left(A\ |\ \overline{B}\right).$ 

$P\left(A\right)=0.59$
$P\left(B\right)=0.46$
$P\left(A\cap B\right)=0.28$
 $find\ \ P\left(\overline{B}\ |\ \overline{A}\right).$ 

Upon arrival at a hospital's emergency room, patients are categorized according to their condition as critical, serious, or stable. In the past year:
(i)10% of the emergency room patients were critical;
(ii) 30% of the emergency room patients were serious;
(iii) The rest of the emergency room patients were stable;
(iv) 40% of the critical patients died;
(v) 10% of the serious patients died; and
(vi) 1% of the stable patients died. 
Given that a patient survived, what is the probability that the patient was categorized as serious upon arrival? 

An insurance company issues life insurance policies in three seperate categories: standard, preferred, and ultra-preferred. Of the company's policyholders, 50% are standard, 40% are preferred, and 10% are ultra-preferred. Each standard policyholder has probability 0.01 of dying in the next year, each preferred policyholder has probability 0.005 of dying in the next year, and each ultra-preferred policyholder has probability 0.001 of dying in the next year. A policyholder dies in the next year. What is the probability that the deceased policyholder was ultra-preferred?

A doctor is studying the relationship between blood pressure and heartbeat abnormalities in her patients. She tests a random sample of her patients and notes their blood pressure (high, low, or normal) and their heartbeat (regular or irregular). She finds that:

(i) 14% have high blood pressure

(ii) 22% have low blood pressure

(iii) 15% have an irregular heartbeat

(iv) Of those with an irregular heartbeat, one-third have high blood pressure

(v) Of those with normal blood pressure, one-eighth have an irregular heartbeat.

What portion of the patients selected have a regular heartbeat and low blood pressure?

The following table give a two-way classification of all graduates of a college in year 2020.

If a person is selected at random from these graduates, find the probability that this person is unemployed.

The following table give a two-way classification of all graduates of a college in year 2020.

If a person is selected at random from these graduates, find the probability that this person is a male.

The following table give a two-way classification of all graduates of a college in year 2020.

If a person is selected at random from these graduates, find the probability that this person is a male who is employed.

The following table give a two-way classification of all graduates of a college in year 2020.

If a person is selected at random from these graduates, find the probability that this person is a male or unemployed.

The following table give a two-way classification of all graduates of a college in year 2020.

If a person is selected at random from these graduates, find the probability that this person is employed given that the person is a female.

The following table give a two-way classification of all graduates of a college in year 2020.

If a person is selected at random from these graduates, find the probability that this person is a male given the person is employed.

The Webster Mail Order Company sells expensive stereos by mail. The following table lists the frequency distribution of the number of orders received per day by this company during the past 100 days,

Find the standard deviation for the probability distribution developed for the number of orders received per day for the past 100 days at the company.

 $F\left(x\right)=\cdots$  

 $0.67,\ 4\le x<5$  

Find the following probability

 $F\left(x\right)=\cdots$  

 $0.67,\ 4\le x<5$  

Find the following probability

 $F\left(x\right)=\cdots$  

 $0.67,\ 4\le x<5$  

Find the following probability

 $F\left(x\right)=\cdots$  

 $0.67,\ 4\le x<5$  

Find the following probability

 $F\left(x\right)=\cdots$  

 $0.67,\ 4\le x<5$  

Find the following probability

 $F\left(x\right)=\cdots$  

 $0.67,\ 4\le x<5$  

Find the following probability

Let X and Y be independent variables with

E(X) = 3,

V(X) = 16,

E(Y) = 10,

V(Y) = 64

Find E(2X+3Y-8)

Let X and Y be independent variables with
E(X) = 3,
V(X) = 16,
E(Y) = 10,
V(Y) = 64

 $Find\ \ \ \ E(2X^2+3Y^2-8)$  

Let X and Y be independent variables with
E(X) = 3,
V(X) = 16,
E(Y) = 10,
V(Y) = 64

 $Find\ \ \ \ V(2X^{ }+3Y^{ }-8)$