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A board game requires players79 Board games and diceto roll a pair of balanced dice for each player's turn.Denote the outcomes by (die 1, die 2), such as5 on die 1 and a 3 on die 2.(5, 3) for aa. List the sample space of the 36 possible outcomes forthe two dice.b. Let A be the event that you roll doubles (that is, eachdie has the same outcome). List the outcomes in Aand find its probability.c. Let B be the event that the sum on the pair of dice is7. Find P(B).d. Find the probability of (i) A and B, (ii) A or B, and(ii) B given A.e. Are events A and B independent, disjoint, or neither?Explain.

Question

Part D and E

 

A board game requires players
79 Board games and dice
to roll a pair of balanced dice for each player's turn.
Denote the outcomes by (die 1, die 2), such as
5 on die 1 and a 3 on die 2.
(5, 3) for a
a. List the sample space of the 36 possible outcomes for
the two dice.
b. Let A be the event that you roll doubles (that is, each
die has the same outcome). List the outcomes in A
and find its probability.
c. Let B be the event that the sum on the pair of dice is
7. Find P(B).
d. Find the probability of (i) A and B, (ii) A or B, and
(ii) B given A.
e. Are events A and B independent, disjoint, or neither?
Explain.
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A board game requires players 79 Board games and dice to roll a pair of balanced dice for each player's turn. Denote the outcomes by (die 1, die 2), such as 5 on die 1 and a 3 on die 2. (5, 3) for a a. List the sample space of the 36 possible outcomes for the two dice. b. Let A be the event that you roll doubles (that is, each die has the same outcome). List the outcomes in A and find its probability. c. Let B be the event that the sum on the pair of dice is 7. Find P(B). d. Find the probability of (i) A and B, (ii) A or B, and (ii) B given A. e. Are events A and B independent, disjoint, or neither? Explain.

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Step 1

a. The sample space of the 36 possible outcomes for the two dice is,

(1,1).(1,2).1,3).(1.4). (1,5). (1,6)
(2,1).(2,2).(2,3).(2,4). (2,5).(2,6)
|(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).(62).(6,3). (6,4). (6, 5). (6,6)
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(1,1).(1,2).1,3).(1.4). (1,5). (1,6) (2,1).(2,2).(2,3).(2,4). (2,5).(2,6) |(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).(62).(6,3). (6,4). (6, 5). (6,6)

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Step 2

b. Let A be the event that you roll doubles. The possible outcomes for event A is,

-{(11).(2,2).(3,3).(4,4). (5,5).(6,6)}
Outcomes for event A
=
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-{(11).(2,2).(3,3).(4,4). (5,5).(6,6)} Outcomes for event A =

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Step 3

The probability of ...

P(APossible number of outcomes
Total number of outcomes
6
36
1
6
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P(APossible number of outcomes Total number of outcomes 6 36 1 6

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