Question

a die is tossed. find the odds against rolling a number greater than 1.
the odds against rolling a number greater than 1 are \boxed{ }:\square.\
(simplify your answer.)

Explanation:

Step1: Determine the number of unfavorable and favorable outcomes

A standard die has 6 faces numbered 1 - 6.
The event of rolling a number greater than 1 has 5 favorable outcomes (\(2,3,4,5,6\)).
The event of not rolling a number greater than 1 (unfavorable) has 1 outcome (\(1\)).

Step2: Calculate the odds against

The formula for odds against an event \(E\) is \(\text{Odds against }E=\frac{\text{Number of unfavorable outcomes}}{\text{Number of favorable outcomes}}\)
Here, number of unfavorable outcomes \(n(U) = 1\), number of favorable outcomes \(n(F)=5\)

Answer:

\(1:5\)