Question

use the given odds to determine the probability of the underlined event. odds against getting injured by falling down stairs: 2,360 to 1 the probability of getting injured by falling down stairs is \boxed{}. (type an integer or a simplified fraction.)

Explanation:

Step1: Recall the formula for probability from odds against

If the odds against an event \(E\) are \(a\) to \(b\), then the probability of the event \(E\), \(P(E)=\frac{b}{a + b}\). Here, \(a = 2360\) (odds against) and \(b = 1\) (odds in favor).

Step2: Substitute the values into the formula

Substitute \(a = 2360\) and \(b = 1\) into \(P(E)=\frac{b}{a + b}\). We get \(P(E)=\frac{1}{2360+1}\).

Step3: Simplify the fraction

\(2360 + 1=2361\), so \(P(E)=\frac{1}{2361}\).

Answer:

\(\frac{1}{2361}\)