Maths-
General
Easy

Question

If A and B are two events such that P left parenthesis A union B right parenthesis equals 5 over 6 comma P left parenthesis A intersection B right parenthesis equals 1 third and P left parenthesis A right parenthesis equals 2 over 3 then A and B are

  1. dependent events
  2. independent events
  3. mutually exclusive events
  4. mutually exclusive and independent events

hintHint:

In this question we have to find what A and B events are if A and B are two events such that P left parenthesis A union B right parenthesis equals 5 over 6 comma P left parenthesis A intersection B right parenthesis equals 1 third and P left parenthesis A right parenthesis equals 2 over 3 .A and B are two events associated with the same random experiment, then A and B are known as independent events if P (A ∩ B) = P(B) .P(A), dependent events if  P(A∩B) = P(A).P(B/A) or P(A∩B) = P(B).P(A/B) and mutually exclusive if P (A ∩ B) =0.

The correct answer is: independent events


    As P left parenthesis A union B right parenthesis equals 5 over 6 comma P left parenthesis A intersection B right parenthesis equals 1 third and P left parenthesis A right parenthesis equals 2 over 3
    P(B)=P (AUB)- P(A) +P (A ∩ B) =5 over 6 minus 2 over 3 plus 1 third equals fraction numerator 5 minus 4 plus 2 over denominator 6 end fraction equals 3 over 6 equals 1 half
    As P(A). P(B)=2 over 3 cross times 1 half equals 1 third equals P left parenthesis A intersection B right parenthesis
    So, A and B are independent events.

    Related Questions to study

    General
    maths-

    Number of rectangles in the grid shown which are not squares is:

    Number of rectangles in the grid shown which are not squares is:

    maths-General
    General
    maths-

    If  P left parenthesis A with not stretchy bar on top right parenthesis equals 0.7 comma P left parenthesis B right parenthesis equals 0.7  and P left parenthesis B divided by A right parenthesis equals 0.5 then P left parenthesis A intersection B right parenthesis equals

    If  P left parenthesis A with not stretchy bar on top right parenthesis equals 0.7 comma P left parenthesis B right parenthesis equals 0.7  and P left parenthesis B divided by A right parenthesis equals 0.5 then P left parenthesis A intersection B right parenthesis equals

    maths-General
    General
    chemistry-

    The correct order of solubility in water is:
    a) CH3OH
    b) CH3CH2OH
    c) 
    d) 

    The correct order of solubility in water is:
    a) CH3OH
    b) CH3CH2OH
    c) 
    d) 

    chemistry-General
    parallel
    General
    chemistry-

    Decreasing order of melting point of compound I - IV follows:
    i) 
    ii) 
    iii) 
    iv) 

    Decreasing order of melting point of compound I - IV follows:
    i) 
    ii) 
    iii) 
    iv) 

    chemistry-General
    General
    chemistry-

    Decreasing order of melting point of compound I to IV follows
    i) 
    ii) 
    iii) 
    iv) 

    Decreasing order of melting point of compound I to IV follows
    i) 
    ii) 
    iii) 
    iv) 

    chemistry-General
    General
    chemistry-

    Identify the correct order of melting point of the following compounds

    Identify the correct order of melting point of the following compounds

    chemistry-General
    parallel
    General
    chemistry-

    Decreasing order of boiling point of I to IV follow
    I) Methyl formate
    II) Ethyl formate
    III) Iso-propylformate
    IV) n-propylformate

    Decreasing order of boiling point of I to IV follow
    I) Methyl formate
    II) Ethyl formate
    III) Iso-propylformate
    IV) n-propylformate

    chemistry-General
    General
    chemistry-

    Decreasing order of boiling point of I to IV follow.
    I) 
    II) 
    III) 
    IV) 

    Decreasing order of boiling point of I to IV follow.
    I) 
    II) 
    III) 
    IV) 

    chemistry-General
    General
    chemistry-

    The correct boiling point order is:



    The correct boiling point order is:



    chemistry-General
    parallel
    General
    chemistry-

    Arrange the following in decreasing order of their boiling points

    Arrange the following in decreasing order of their boiling points

    chemistry-General
    General
    chemistry-

    Decreasing order of boiling point of I - IV follows

    Decreasing order of boiling point of I - IV follows

    chemistry-General
    General
    chemistry-

    Correct boiling point order for I to IV is:
    I) CH subscript 3 straight F
    II) CH subscript 3 Br
    III) CH3Cl
    IV) CH3I

    Correct boiling point order for I to IV is:
    I) CH subscript 3 straight F
    II) CH subscript 3 Br
    III) CH3Cl
    IV) CH3I

    chemistry-General
    parallel
    General
    chemistry-

    The correct order of dipole moment is:

    The correct order of dipole moment is:

    chemistry-General
    General
    chemistry-

    The increasing order of dipole moment of following compounds is :



    The increasing order of dipole moment of following compounds is :



    chemistry-General
    General
    chemistry-

    Arrange the following in decreasing order of dipole moments.
    i) 
    ii) 
    iii) 

    Arrange the following in decreasing order of dipole moments.
    i) 
    ii) 
    iii) 

    chemistry-General
    parallel

    card img

    With Turito Academy.

    card img