Question

if you are given odds of 4 to 5 in favor of winning a bet, what is the probability of winning the bet? the probability is (type an integer or a simplified fraction.)

Explanation:

Step1: Recall odds - probability relationship

Odds in favor of an event $E$ is given by $\frac{P(E)}{1 - P(E)}$. Here, odds in favor of winning is $\frac{4}{5}$. Let $P$ be the probability of winning. So, $\frac{P}{1 - P}=\frac{4}{5}$.

Step2: Cross - multiply

Cross - multiplying the equation $\frac{P}{1 - P}=\frac{4}{5}$ gives $5P = 4(1 - P)$.

Step3: Expand and solve for $P$

Expand the right - hand side: $5P=4 - 4P$. Add $4P$ to both sides: $5P + 4P=4$, which simplifies to $9P = 4$. Then $P=\frac{4}{9}$.

Answer:

$\frac{4}{9}$