Question

if you are given odds of 3 to 4 in favor of winning a bet, what is the probability of winning the bet?

the probability is \boxed{}.
(type an integer or a simplified fraction.)

Explanation:

Step1: Recall the formula for probability from odds

If the odds in favor of an event \(E\) are \(a\) to \(b\), the probability \(P(E)=\frac{a}{a + b}\). Here, \(a = 3\) (number of favorable outcomes) and \(b=4\) (number of unfavorable outcomes).

Step2: Calculate the probability

Substitute \(a = 3\) and \(b = 4\) into the formula \(P(E)=\frac{a}{a + b}\). So, \(P(E)=\frac{3}{3+4}\).

Answer:

\(\frac{3}{7}\)