Question

the probability of an event not happening is 5/8. what are the odds for that event? a) 5/3 b) 3/5 c) 5/8 d) 8/

Explanation:

Step1: Find the probability of the event happening

The probability of an event \(E\) not happening, \(P(\text{not }E)=\frac{5}{8}\).
Using the formula \(P(E)+P(\text{not }E) = 1\), we get \(P(E)=1 - P(\text{not }E)\).
So, \(P(E)=1-\frac{5}{8}=\frac{8 - 5}{8}=\frac{3}{8}\).

Step2: Calculate the odds for the event

The odds for an event \(E\) is given by the formula \(\text{Odds for }E=\frac{P(E)}{P(\text{not }E)}\).
Substituting \(P(E)=\frac{3}{8}\) and \(P(\text{not }E)=\frac{5}{8}\), we have \(\text{Odds for }E=\frac{\frac{3}{8}}{\frac{5}{8}}\).
Since \(\frac{\frac{3}{8}}{\frac{5}{8}}=\frac{3}{8}\times\frac{8}{5}=\frac{3}{5}\).

Answer:

B. \(3/5\)