Please hurry 14PTS 3 QUESTIONS
-Two six-sided number cubes are rolled. What is the probability that a sum of 7 is rolled? Express your answer as a fraction in simplest form.
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Two six-sided number cubes are rolled. What is the probability that a product of 12 is rolled? Express your answer as a decimal. Round to the nearest hundredth if necessary.

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a) 1/6 b) 0.11

Step-by-step explanation:

Probability is the likelihood or chance that an event will occur.

Probability = Expected outcome of event/Total outcome

If a two six-sided number cubes are rolled e.g 2dice, the total number of sample space is expressed as 6^n where n is 2(since only 2 six sided cubes are rolled)

Total outcome of event = 6² = 36

If sum of 7 are generated after rolling, the expected outcome will be:

E = {(1,6),(6,1),(2,5),(5,2),(3,4),(4,3)}

Note that each of the list will given a sum of 7

Total expected outcome = 6

Probability that a sum of 7 is rolled

= 6/36

= 1/6

b) Similarly, if a product of 12 is rolled, the expected outcome of event are:

E = {(2,6),(6,2),(3,4),(4,3)}

Expected outcome = 4

Note that the product of each outcome will give us 12.

Probability that a product of 12 is rolled = 4/36

= 1/9

= 0.11 (to nearest hundredth)

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step-by-step explanation: