Chapter 5, Problem 1CR

StatisticalLiteracy Consider the following two events for an individual: A = owns a cell phone B = owns a laptop computer

Translate each event into words.

(a) $A^c$(d) A\B

(b) A and B(c) B\A

(c)A or B

To determine

The translation of $A^c$ into words.

Answer to Problem 1CR

Solution: The individual does not own a cell phone.

Explanation of Solution

Given: A = the event that an individual owns a cell phone.

The complement of an event A is denoted as $A^c$.

According to the provided information for an individual, the event A is defined as ‘owns a cellphone’. So, the complement of event A is ‘the individual does not own a cellphone’.

To determine

The translation of $A\text{ and }B$ into words.

Answer to Problem 1CR

Solution: The event that an individual owns a cell phone and a laptop computer.

Explanation of Solution

Given: A = an individual owns a cell phone, B = an individual owns a laptop computer.

Both the events A and B, occurring together is denoted as $\left(A\text{ and }B\right)$.

According to the provided information for an individual, the event A is defined as ‘owns a cellphone’ and the event B is defined as ‘owns a laptop computer’. So, both the events A and B occurring together can be defined as ‘the individual owns a cellphone and a laptop computer’.

To determine

The translation of $A\text{ or }B$ into words.

Answer to Problem 1CR

Solution: The individual owns either a cell phone or a laptop computer or both.

Explanation of Solution

Given: A = an individual owns a cell phone, B = an individual owns a laptop computer.

The occurrence of either event A or B or both is denoted as $\left(A\text{ or }B\right)$.

According to the provided information for an individual, the event A is defined as ‘owns a cellphone’ and the event B is defined as ‘owns a laptop computer’. So, the occurrence of either event can be defined as ‘the individual owns a cellphone or a laptop computer or both’.

To determine

The translation of $A|B$ into words.

Answer to Problem 1CR

Solution: The individual is a laptop computer owner who owns a cellphone.

Explanation of Solution

Given: A = an individual owns a cell phone, B = an individual owns a laptop computer.

The occurrence of event A given that event B has occurred is denoted as $\left(A|B\right)$.

According to the provided information for an individual, the event A is defined as ‘owns a cellphone’ and the event B is defined as ‘owns a laptop computer’. So, the occurrence of A given that event B has occurred is defined as ‘the individual who is an owner of a laptop computer, owns a cellphone’.

To determine

The translation of $B|A$ into words.

Answer to Problem 1CR

Solution: The individual is a cellphone owner who owns a laptop computer.

Explanation of Solution

Given: A = an individual owns a cell phone, B = an individual owns a laptop computer.

The occurrence of event B given that the event A has occurred is denoted as $\left(B|A\right)$.

According to the provided information for an individual, the event A is defined as ‘owns a cellphone’ and the event B is defined as ‘owns a laptop computer’. So, the occurrence of event B given that event A has occurred can be defined as ‘the individual who is an owner of a cellphone, owns a laptop computer’.