Question

find the odds for rolling a 6 - sided die and getting a 4. to find the odds against rolling a 6 - sided die and getting a 4. to simplify your answers. question help: video message instructor

Explanation:

Step1: Calculate the number of favorable and unfavorable outcomes for odds for

When rolling a 6 - sided die, the total number of outcomes \(n = 6\). The number of favorable outcomes (getting a 4) \(m=1\). The number of unfavorable outcomes \(k = 6 - 1=5\).
The formula for odds for an event \(E\) is \(\text{Odds for }E=\frac{\text{Number of favorable outcomes}}{\text{Number of unfavorable outcomes}}\).
So, \(\text{Odds for getting a 4}=\frac{1}{5}\), which is \(1\) to \(5\).

Step2: Calculate the number of favorable and unfavorable outcomes for odds against

The formula for odds against an event \(E\) is \(\text{Odds against }E=\frac{\text{Number of unfavorable outcomes}}{\text{Number of favorable outcomes}}\).
Since the number of unfavorable outcomes \(k = 5\) and the number of favorable outcomes \(m = 1\), \(\text{Odds against getting a 4}=\frac{5}{1}\), which is \(5\) to \(1\).

Answer:

• Odds for: \(1\) to \(5\)
• Odds against: \(5\) to \(1\)