English

(B) a and B Are Two Events Such that P (A) = 0.54, P (B) = 0.69 and P (A ∩ B) = 0.35. Find (Iii) P (A ∩ ¯ B ) - Mathematics

Advertisements
Advertisements

Question

A and B are two events such that P (A) = 0.54, P (B) = 0.69 and P (A ∩ B) = 0.35. Find  
P (A ∩  \[\bar{ B } \] )

Solution

Given:
P (A) = 0.54, P (B) = 0.69 and P (A ∩ B) = 0.35

\[P\left( A \cap \bar{B} \right) = P\left( A \right) - P\left( A \cap B \right)\]

                         = 0.54 - 0.35
                         = 0.19

 

shaalaa.com
  Is there an error in this question or solution?
Chapter 33: Probability - Exercise 33.4 [Page 67]

APPEARS IN

RD Sharma Mathematics [English] Class 11
Chapter 33 Probability
Exercise 33.4 | Q 1.2 | Page 67

Video TutorialsVIEW ALL [1]

RELATED QUESTIONS

Three coins are tossed once. Let A denote the event "three heads show", B denote the event "two heads and one tail show". C denote the event "three tails show" and D denote the event "a head shows on the first coin". Which events are

  1. mutually exclusive?
  2. simple?
  3. compound?

In a single throw of a die describe the event:

 C = Getting a multiple of 3


In a single throw of a die describe the event:

D = Getting a number less than 4


In a single throw of a die describe the event:

E = Getting an even number greater than 4


In a single throw of a die describe the event:

F = Getting a number not less than 3.
Also, find A ∪ BA ∩ BB ∩ CE ∩ FD ∩ F and \[ \bar { F } \] . 

 


A and B are two events such that P (A) = 0.54, P (B) = 0.69 and P (A ∩ B) = 0.35. Find
P (A ∪ B).


A and B are two events such that P (A) = 0.54, P (B) = 0.69 and P (A ∩ B) = 0.35. Find

\[P (\bar{ A } \cap \bar{ B } )\]


A dice is thrown twice. What is the probability that at least one of the two throws come up with the number 3?


If three dice are throw simultaneously, then the probability of getting a score of 5 is


If P(A ∪ B) = P(A ∩ B) for any two events A and B, then


An experiment consists of rolling a die until a 2 appears. How many elements of the sample space correspond to the event that the 2 appears not later than the k th roll of the die?


In a large metropolitan area, the probabilities are 0.87, 0.36, 0.30 that a family (randomly chosen for a sample survey) owns a colour television set, a black and white television set, or both kinds of sets. What is the probability that a family owns either anyone or both kinds of sets?


A team of medical students doing their internship have to assist during surgeries at a city hospital. The probabilities of surgeries rated as very complex, complex, routine, simple or very simple are respectively, 0.15, 0.20, 0.31, 0.26, .08. Find the probabilities that a particular surgery will be rated complex or very complex 


A team of medical students doing their internship have to assist during surgeries at a city hospital. The probabilities of surgeries rated as very complex, complex, routine, simple or very simple are respectively, 0.15, 0.20, 0.31, 0.26, .08. Find the probabilities that a particular surgery will be rated neither very complex nor very simple 


A team of medical students doing their internship have to assist during surgeries at a city hospital. The probabilities of surgeries rated as very complex, complex, routine, simple or very simple are respectively, 0.15, 0.20, 0.31, 0.26, .08. Find the probabilities that a particular surgery will be rated routine or complex


A team of medical students doing their internship have to assist during surgeries at a city hospital. The probabilities of surgeries rated as very complex, complex, routine, simple or very simple are respectively, 0.15, 0.20, 0.31, 0.26, .08. Find the probabilities that a particular surgery will be rated routine or simple


One urn contains two black balls (labelled B1 and B2) and one white ball. A second urn contains one black ball and two white balls (labelled W1 and W2). Suppose the following experiment is performed. One of the two urns is chosen at random. Next a ball is randomly chosen from the urn. Then a second ball is chosen at random from the same urn without replacing the first ball. Write the sample space showing all possible outcomes


One urn contains two black balls (labelled B1 and B2) and one white ball. A second urn contains one black ball and two white balls (labelled W1 and W2). Suppose the following experiment is performed. One of the two urns is chosen at random. Next a ball is randomly chosen from the urn. Then a second ball is chosen at random from the same urn without replacing the first ball. What is the probability that two black balls are chosen?


A sample space consists of 9 elementary outcomes e1, e2, ..., e9 whose probabilities are 
P(e1) = P(e2) = 0.08, P(e3) = P(e4) = P(e5) = 0.1
P(e6) = P(e7) = 0.2, P(e8) = P(e9) = 0.07
Suppose A = {e1, e5, e8}, B = {e2, e5, e8, e9}
Calculate P(A), P(B), and P(A ∩ B)


A sample space consists of 9 elementary outcomes e1, e2, ..., e9 whose probabilities are 
P(e1) = P(e2) = 0.08, P(e3) = P(e4) = P(e5) = 0.1
P(e6) = P(e7) = 0.2, P(e8) = P(e9) = 0.07
Suppose A = {e1, e5, e8}, B = {e2, e5, e8, e9}
List the composition of the event A ∪ B, and calculate P(A ∪ B) by adding the probabilities of the elementary outcomes.


A sample space consists of 9 elementary outcomes e1, e2, ..., e9 whose probabilities are 
P(e1) = P(e2) = 0.08, P(e3) = P(e4) = P(e5) = 0.1
P(e6) = P(e7) = 0.2, P(e8) = P(e9) = 0.07
Suppose A = {e1, e5, e8}, B = {e2, e5, e8, e9}
Calculate `P(barB)` from P (B), also calculate `P(barB)` directly from the elementary outcomes of `barB`


Determine the probability p, for the following events. 
At least one head appears in two tosses of a fair coin.


Determine the probability p, for the following events. 
The sum of 6 appears in a single toss of a pair of fair dice.


If P(A ∪ B) = P(A ∩ B) for any two events A and B, then ______.


The probability that at least one of the events A and B occurs is 0.6. If A and B occur simultaneously with probability 0.2, then `P(barA) + P(barB)` is ______.


The probability of an occurrence of event A is 0.7 and that of the occurrence of event B is 0.3 and the probability of occurrence of both is 0.4


Let S = {1, 2, 3, 4, 5, 6} and E = {1, 3, 5}, then `barE` is ______.


If A and B are two events associated with a random experiment such that P(A) = 0.3, P(B) = 0.2 and P(A ∩ B) = 0.1, then the value of `P(A ∩ barB)` is ______.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×