Question

In: Statistics and Probability

Suppose you roll, two 6-sided dice (refer back to the sample space in the sample space...

Suppose you roll, two 6-sided dice (refer back to the sample space in the sample space notes). Write any probability as a decimal to three place values and the odds using a colon. Determine the following:

a. the probability that you roll a sum of seven (7) is .

b. The odds for rolling a sum of four (4) is .

c. The odds against the numbers on both dice being the same is .

Solutions

Expert Solution

When two 6-sided dice are rolled: Total number of outcomes = 6 x 6 =36

a.

Probability that you roll a sum of seven (7)

= Number of ocutomes that favor a sum of seven / Total number of outcomes

Outcomes that favor a sum of seven : (1,6),(2,5),(3,4),(4,3),(5,2),(6,1)

Number of Outcomes that favor a sum of seven = 6

Probability that you roll a sum of seven (7)

= Number of ocutomes that favor a sum of seven / Total number of outcomes = 6/36 = 1/6 = 0.167

Probability that you roll a sum of seven (7) is 0.167

b .

The odds of rolling a sum of four (4)

= Number of outcomes that favor a sum of four (4) : Number of outcomes that do not favor a sum of (4)

Outcomes that favor a sum of four (4) : (1,3),(2,2),(3,1)

Number of outcomes that favor a sum of four(4) = 3

Number of outcomes that do not favor a sum of (4)

= Total number of outcomes - Number of outcomes that favor a sum of four(4) = 36-3 =33

The ods of rolling a sum of four is

Number of outcomes that favor a sum of four(4) : Number of outcomes that do not favor a sum of (4) = 3 : 33

The odds of rolling a sum of four (4) is 3 : 33 or 1:11

c. The odds against the numbers on both dice being the same is .

Outcomes that favor numbers on both dice being the same = (1,1),(2,2),(3,3),(4,4),(5,5),(6,6)

Number of outcomes that favor numbers on both dice being the same = 6

Number of outcomes that do not favor numbers on both dice being the same

=Total number of outcomes -  Number of outcomes that favor numbers on both dice being the same

=36-6=30

The odds against the numbers on both dice being the same is .

Number of outcomes that do not favor numbers on both dice being the same : Number of outcomes that favor numbers on both dice being the same

: 30:6 ; 5:1

The odds against the numbers on both dice being the same is . 30:6 or 5:1

orchestra answered 1 year ago
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