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Sagot :
Answer:
The odds are 12
Step-by-step explanation:
The odds of rolling an odd number from the sum of two rolls requires that we roll one even number from one die and an odd number from another die.
Thus the probability of the event is P(e) = 1/12.
What is probability?
Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one.
For the given situation,
The sample space for rolling two 6 sided dice is
[tex]s[/tex] = { [tex](1,1),(1,2),(1,3),(1,4),(1,5),(1,6)[/tex]
[tex](2,1),(2,2),(2,3),(2,4),(2,5),(2,6)[/tex]
[tex](3,1),(3,2),(3,3),(3,4),(3,5),(3,6)[/tex]
[tex](4,1),(4,2),(4,3),(4,4),(4,5),(4,6)[/tex]
[tex](5,1),(5,2),(5,3),(5,4),(5,5),(5,6)[/tex]
[tex](6,1),(6,2),(6,3),(6,4),(6,5),(6,6)[/tex]}
So, [tex]n(s)=36[/tex]
Let the event be the probability that the sum is odd and the number on one of the dice is a 5
Consider that the probability that the sum is odd be a,
[tex]a =[/tex] { [tex](1,2),(1,4),(1,6),(2,1),(2,3),(2,5),(3,2),(3,4),(3,6),\\[/tex]
[tex](4,1),(4,3),(4,5),(5,2),(5,4),(5,6),(6,1),(6,3),(6,5) }[/tex] }
Consider that the probability that the number on one of the dice is 5 be b,
[tex]b=[/tex] { [tex](1,5),(2,5),(3,5),(4,5),(5,5),(6,5)[/tex] }
The probability of the event can be find by taking intersection of a and b
⇒[tex]e=a[/tex]∩[tex]b[/tex] = { [tex](2,5),(4,5),(6,5)[/tex] }
⇒[tex]n(e)[/tex] [tex]=3[/tex]
Probability (event )=[tex]\frac{n(e)}{n(s)}[/tex]
⇒[tex]p(e)=\frac{3}{36}[/tex]
⇒[tex]p(e)=\frac{1}{12}[/tex]
Hence we can conclude that the probability of the event is P(e) = 1/12
Learn more about probability here
https://brainly.com/question/13604758
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