Question

suppose the odds in favor of a person who is alive at age 20 will being alive at age 70 are 125 to 225. find the probability that a person who is alive at age 20 will be alive at age 70. the probability is (type an integer or a simplified fraction.)

Explanation:

Step1: Recall odds - probability relationship

If the odds in favor of an event $E$ are $a$ to $b$, then the probability of the event $E$ is given by $P(E)=\frac{a}{a + b}$.
Here, $a = 125$ and $b=275$.

Step2: Calculate the probability

Substitute $a = 125$ and $b = 275$ into the formula $P=\frac{a}{a + b}$.
$P=\frac{125}{125+275}=\frac{125}{400}$.
Simplify the fraction $\frac{125}{400}$ by dividing both the numerator and the denominator by their greatest - common divisor, which is 25.
$\frac{125\div25}{400\div25}=\frac{5}{16}$.

Answer:

$\frac{5}{16}$