Question

This question is due my 11:50pm EST One die is rolled 2 times in a row.          The observation is the number that comes up on each roll (rolling 2 and 5 is not the same as rolling 5 and 2).

Describe one outcome and find a number of outcomes. Write all outcomes of the sample space S   (you can use … notation to indicate many numbers of cases).      : “pairs are rolled” (both dice come up the same number)     Write the event as a set,    compute the event probability,    and    odds. : “the sum is 6 or 7”                Write the event as a set,     compute the event probability,    and    odds. : “the sum is even number”  Write the event as a set,     compute the event probability,    and    odds.

Answer 1

a) The sample space of all the outcomes in the sample space here is given as:
S = {11, 12, 13, 14, 15, 16,
21, 22, 23, 24, 25, 26,
31, 32, 33, 34, 35, 36,
41, 42, 43, 44, 45, 46,
51, 52, 53, 54, 55, 56,
61, 62, 63, 64, 65, 66 }

b) The sample space for outcomes where pairs are rolled is obtained here as:
S = {11, 22, 33, 44, 55, 66}

c) The sum if 6 or 7. The outcomes for this event here are given as:
X = {15, 24, 33, 42, 51,
16, 25, 34, 43, 52, 61}

Therefore the probability here is computed as:
= Number of outcomes in event X / Total number of outcomes in sample space
= 11/36

Therefore 11/36 is the required probability here.

The odds for the above event are computed here as:
= Number of outcomes in event X / Number of events not in X but are in S
= 11/ (36-11)
= 11/25

Therefore 11/25 are the required odds here.

d) The sum is an even number here. The outcome here are given as:
Y = {11, 13, 15, 22, 24, 26,
31, 33, 35, 42, 44, 46,
51, 53, 55, 62, 64, 66 }

As there are 18 outcomes here,
probability is computed as: = 18/36 = 0.5
Therefore 0.5 is the required probability here.

As the probability is 0.5, the odds here is computed as: 1:1

Therefore 1:1 are the required odds here.