Answer :
Answer:
Odds for = Odds against = 1/2
Step-by-step explanation:
In a fair die, we have {1, 2, 3, 4, 5, 6} and [tex]$ n(S) = 6 $[/tex]
{1, 4, 5} and {2, 3, 6} constitute the entire sample space.
So, Probability of getting a 1 or a 4 or a 5
= Probability of getting a 1 +
Probability of getting a 4 +
Probability of getting a 5
= [tex]$ \frac{1}{6} + \frac{1}{6} + \frac{1}{6} $[/tex]
=[tex]$ \frac{3}{6} = \frac{1}{2} $[/tex]
Therefore, Odds for 1 or 4 or 5 = [tex]$ \frac{1}{2} $[/tex].
Since, Probability of getting a number between 1 and 6 is 1 and Probability of getting a number from 2 or 3 or 6 = [tex]$ \frac{1}{2} $[/tex], we have:
Probability of not getting a 1 or 4 or 5 = 1 - [tex]$ \frac{1}{2} $[/tex]
= [tex]$ \frac{1}{2} $[/tex]
Hence, odds for and odds against = [tex]$ \frac{1}{2} $[/tex]