Given the following: P(A) = 0.3 P(B) = 0.2 P(A or B) = 0.5 P(A and B) = 0 Which of the following is true? A and B are disjoint. A and B are neither disjoint nor independent.A and B are independent. A and B are disjoint and independent.

coexpennan 2021-01-08 Answered

Given the following: P(A)=0.3P(B)=0.2P(A or B)=0.5P(A and B)=0
Which of the following is true?
A and B are disjoint.
A and B are neither disjoint nor independent.
A and B are independent.
A and B are disjoint and independent.

You can still ask an expert for help

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Solve your problem for the price of one coffee

  • Available 24/7
  • Math expert for every subject
  • Pay only if we can solve it
Ask Question

Expert Answer

Mayme
Answered 2021-01-09 Author has 103 answers

Given: P(A)=0.3
P(B)=0.2
P(A or B)=0.5
P(A and B)=0
Two events are disjoint, if the events cannot occur at the same time. Since P(A and B)=0, the events A and B cannot occur at the same time and thus events A and B are disjoint.
Two events are independent, if the probability that one event occur in no way affects the probability of the other event ocuring.
Moreover, two events are intependent if and only if P(A and B)=P(A)P(B).
P(A)P(B)=0.302=0.06
P(A and B)=0
Since 0.060, the events A and B are not independent. Thus the answer is then: A and B are disjoint.

Not exactly what you’re looking for?
Ask My Question

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Relevant Questions

asked 2021-09-09
In a fuel economy study, each of 3 race cars is tested using 5 different brands of gasoline at 7 test sites located in different regions of the country. If 2 drivers are used in the study, and test runs are made once under each distinct set of conditions, how many test runs are needed?
asked 2021-09-08
A restaurant offers a $12 dinner special that has 7 choices for an appetizer, 12 choices for an entree, and 6 choices for a dessert. How many different meals are available when you select an appetizer, an entree,and a dessert?
asked 2021-09-01
A company has 34 salespeople. A board member at the company asks for a list of the top 5 salespeople, ranked in order of effectiveness. How many such rankings are possible?
asked 2021-01-19
Suppose the alphabet consists of just {a,b,c,d,e}. Consider strings of letters that show repetitions. How many 4-letter strings are there that do not contain “aa"?
asked 2022-05-21
With a standard 52 deck (13 types and 4 suites), what is the probability that a poker hand contains cards of five different types? A poker hand is a set of 5 cards.
The obvious answer is A / B where A is the number of poker hands that have 5 different types of cards and B is the total number of poker hands which is C(52,5).
Right now I think A = C(13,5) since there are 13 different types of cards I choose 5 from them but I am unsure if A = 4 * C(13,5) instead, where 4 is the different suites.
asked 2022-06-03
Let m , n 0 be two integers. Prove that
k = m n ( 1 ) k m ( k m ) ( n k ) = δ m n
where δ m n defined by δ m n = { 1 , if  m = n ; 0 , if  m n
asked 2021-01-10
The problem reads: Suppose P(X1)=.75 and P(Y2X1)=.40. What is the joint probability of X1 and Y2?
This is how I answered it. P(X1 and Y2) =P(X1)×P(Y1X1)=.75×.40=0.3.
What I don't understand is how do you get the P(Y1X1)? I am totally new to Statistices and I need to understand each part of the process in order to get the whole concept. Can anyone help me to understand why the P and X exist and what they represent?