18. A pair of fair dice is cast. Let E denote the event that the numberfalling uppermost in the first die is 4 and let F denote the event that thesum of the numbers falling uppermost is 6.(A)59(B) Compute P(EN F).12(A) Compute P(F).10 (0)Sabono nv(D) Compute P(E).(C) Compute P(F|E).ne 2yez01 bilrteiWsst(E) Are E and F independent events?ont Bmod25 poudong sid)d:do eri 0.0 al 1eyodosh

Question
Asked Nov 6, 2019
18. A pair of fair dice is cast. Let E denote the event that the number
falling uppermost in the first die is 4 and let F denote the event that the
sum of the numbers falling uppermost is 6.
(A)
59
(B) Compute P(EN F).
12
(A) Compute P(F).
10 (0)
Sabo
no nv
(D) Compute P(E).
(C) Compute P(F|E).
ne 2y
ez01 bilrt
ei
Wsst
(E) Are E and F independent events?
ont Bmod
25 po
udong sid)
d:do eri 0.0 al 1ey
odosh
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18. A pair of fair dice is cast. Let E denote the event that the number falling uppermost in the first die is 4 and let F denote the event that the sum of the numbers falling uppermost is 6. (A) 59 (B) Compute P(EN F). 12 (A) Compute P(F). 10 (0) Sabo no nv (D) Compute P(E). (C) Compute P(F|E). ne 2y ez01 bilrt ei Wsst (E) Are E and F independent events? ont Bmod 25 po udong sid) d:do eri 0.0 al 1ey odosh

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Expert Answer

Step 1

Note:

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Step 2

Random experiment of rolling a pair of dice:

Sample space:

The set of all possible outcomes of a probability experiment is called sample space of the experiment.

Here, two fair dice are rolled.

The total number of outcomes in the sample space be n(S) = 62 = 36. That is, there will be 36 equally likely outcomes.

Outcomes will be occurred in ordered pairs. First number in each ordered pair represents the number on the first die and second number in each ordered pair represents the number on the second die. Each of the two numbers can take values 1 to 6.

The sum of the numbers on the dice will be 2, 3, 4, 5, 6, 7, 8, 9, 10 and 11.

The sample space for the experiment is given below:

The possible outcomes for the sum to be 2:(1,1)
The possible outcomes for the sum to be 3:{(1,2).(2,1
The possible outcomes for the sum to be 4:{(1,3),(2,2),(3,1)}
The possible outcomes for the sum to be 5:{1,4),(2,3).(3,2).(4,1)
The possible outcomes for the sum to be 6:{(1,5).(2,4),(3,3).(4, 2), (5,1)}
The possible outcomes for the sum to be 7:{(1,6),(2,5),(3,4),(4,3),(5,2).(6,1)}
The possible outcomes for the sum to be 8:{(2,6),(3,5),(4,4). (5,3).(6,2)}
The possible outcomes for the sum to be 9:{(3,6),(4,5).(5,4), (6,3)
The possible outcomes for the sum to be 10:{(4,6),(5,5).(6,4)
The possible outcomes for the sum to be 11:{(5,6).(6,5)}
The possible outcomes for the sum to be 12:{(6,6)
(1.1),(1,2).(1,3)(1,4),(1.5).(16). (2,1), (2,2).(2,3), (2,4).(2,5). (2,6),
Sample space S (3,1), (3,2),(3,3), (3,4),(3,5),(3,6). (4,1) (4, 2).(4,3).(4,4),(4,5).(4,6);
|(5,1).(5,2).(5,3),(5,4).(5,5).(5,6).(6,1). (6,2),(6,3).(6,4), (6,5),(6,6)
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The possible outcomes for the sum to be 2:(1,1) The possible outcomes for the sum to be 3:{(1,2).(2,1 The possible outcomes for the sum to be 4:{(1,3),(2,2),(3,1)} The possible outcomes for the sum to be 5:{1,4),(2,3).(3,2).(4,1) The possible outcomes for the sum to be 6:{(1,5).(2,4),(3,3).(4, 2), (5,1)} The possible outcomes for the sum to be 7:{(1,6),(2,5),(3,4),(4,3),(5,2).(6,1)} The possible outcomes for the sum to be 8:{(2,6),(3,5),(4,4). (5,3).(6,2)} The possible outcomes for the sum to be 9:{(3,6),(4,5).(5,4), (6,3) The possible outcomes for the sum to be 10:{(4,6),(5,5).(6,4) The possible outcomes for the sum to be 11:{(5,6).(6,5)} The possible outcomes for the sum to be 12:{(6,6) (1.1),(1,2).(1,3)(1,4),(1.5).(16). (2,1), (2,2).(2,3), (2,4).(2,5). (2,6), Sample space S (3,1), (3,2),(3,3), (3,4),(3,5),(3,6). (4,1) (4, 2).(4,3).(4,4),(4,5).(4,6); |(5,1).(5,2).(5,3),(5,4).(5,5).(5,6).(6,1). (6,2),(6,3).(6,4), (6,5),(6,6)

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Step 3

A)Calculating P(F):

Event E denotes that the number falling uppermost in the first die is 4 and F denote that the sum of...

5
P(F)=
36
=0.1389
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5 P(F)= 36 =0.1389

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