Question

Find the odds for and the odds against the event rolling a fair die and getting a 1, a 4,or a 5

Answer 1

Answer:

Odds for = Odds against = 1/2

Step-by-step explanation:

In a fair die, we have {1, 2, 3, 4, 5, 6} and $n(S) = 6$

{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

= $\frac{1}{6} + \frac{1}{6} + \frac{1}{6}$

=$\frac{3}{6} = \frac{1}{2}$

Therefore, Odds for 1 or 4 or 5 = $\frac{1}{2}$.

Since, Probability of getting a number between 1 and 6 is 1 and Probability of getting a number from 2 or 3 or 6 = $\frac{1}{2}$, we have:

Probability of not getting a 1 or 4 or 5 = 1 - $\frac{1}{2}$

= $\frac{1}{2}$

Hence, odds for and odds against = $\frac{1}{2}$