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Chirag Pranab Rout
Asked: 2022-11-09T11:48:03+05:30 In:

Two fair dice are rolled. Let `P(A_(i))gt0` donete the event that the sum of the faces of the dice is divisible by i.
For which one of the following (I,j) are the events `A_(i)and A_(j)` independent ?
A. `(3,4)`
B. `(4,6)`
C. `(2,3)`
D. `(4,2)`

Two fair dice are rolled. Let `P(A_(i))gt0` donete the event that the sum of the faces of the dice is divisible by i.
For which one of the following (I,j) are the events `A_(i)and A_(j)` independent ?
A. `(3,4)`
B. `(4,6)`
C. `(2,3)`
D. `(4,2)`
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  1. Correct Answer – C
    `P(A_(2))=1/2,P(A_(3))=1/3,P(A_(6))=1/6`
    `thereforeP(A_(2)nnA_(3))=P(A_(2))P(A_(3))`
    `impliesP(A_(6))=P(A_(2))P(A_(3))`
    `6/36=1/2xx1/3`
    Hence, `A_(2)and A_(3)` are independent.

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Vaishali Mannan
Asked: 2022-11-07T20:50:42+05:30 In:

Two fair dice are rolled. Let `P(A_(i))gt0` donete the event that the sum of the faces of the dice is divisible by i.
The number of all possible ordered pair (I,j) for which the events `A_(i) and a_(j)` are independent is
A. 6
B. 12
C. 13
D. 25

Two fair dice are rolled. Let `P(A_(i))gt0` donete the event that the sum of the faces of the dice is divisible by i.
The number of all possible ordered pair (I,j) for which the events `A_(i) and a_(j)` are independent is
A. 6
B. 12
C. 13
D. 25
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  1. Correct Answer – D
    Note that `A_(1)` is independent with all events `A_(1),A_(2),A_(3),A_(4)….,A_(12),` Now, total number of ordered pairs is 23.
    `underset(22)( underbrace((1.1),(1,2),(1.3),…,(1,11)))+(1,12)`
    Also that `A_(2),A_(3),andA_(3),A_(2)` are independent. Hence, there are 25 ordered pairs.

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Tarun Rao Nayar
Asked: 2022-10-29T20:37:12+05:30 In:

Two fair dice are rolled. Let `P(A_(i))gt0` donete the event that the sum of the faces of the dice is divisible by i.
Which one of the following events is most probable?
A. `A_(3)`
B. `A_(4)`
C. `A_(5)`
D. `A_(6)`

Two fair dice are rolled. Let `P(A_(i))gt0` donete the event that the sum of the faces of the dice is divisible by i.
Which one of the following events is most probable?
A. `A_(3)`
B. `A_(4)`
C. `A_(5)`
D. `A_(6)`
Parabola
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  1. Correct Answer – A
    `P(A_(2))=18/36,`
    `P(A_(3))=12/36=1/3,`
    `P(A_(4))=9/36=1/4`
    `P(A_(5))=7/36`
    `P(A_(6))=6/36=1/6`
    Hence, `A_(3)` is most probable.

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