Two six-sided dice are rolled and their product is taken. How many elements are in the subset of even numbers?

Destinee Bryan
2022-04-10
Answered

Two six-sided dice are rolled and their product is taken. How many elements are in the subset of even numbers?

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Kaitlynn Craig

Answered 2022-04-11
Author has **13** answers

Step 1

When two six-sided dice are rolled the sample space is as shown below

$(1,1),(1,2),(1,3),(1,4),(1,5)(1,6)$

$(2,1),(2,2),(2,3),(2,4),(2,5),(2,6)$

$(3,1),(3,2),(3,3),(3,4),(3,5),(3,6)$

$(4,1),(4,2),(4,3),(4,4),(4,5).(4,6)$

$(5,1).(5,2),(5,3),(5,4),(5,5).(5,6)$

$(6,1),(6,2),(6,3),(6,4),(6,5),(6,6)$

Step 2The subset of the elements where the product is even is shown below

$[(1,2),(1,4),(1,6),(2,1)(2,2)(2,3),(2,4)$

$(2,5),(2,6),(3,2),(3,4),(3,6),(4,1),(4,2)$

$(4,3),(4,4),(4,5),(4,6),(5,2),(5,4),(5,6)$

$(6,1),(6,2),(6,3),(6,4),(6,5).(6,6)]$

Therefore of elements in the subset of even numbers=27

When two six-sided dice are rolled the sample space is as shown below

Step 2The subset of the elements where the product is even is shown below

Therefore of elements in the subset of even numbers=27

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