Question

question 27
suppose the probability of event a are ( p(a)=\frac{17}{50} ).
a) the odds in favor of event a happening are to.
b) the odds against event a happening are to.
enter your answers as whole numbers.
question help: video message instructor

Explanation:

Step1: Calculate the probability of event \(A\) not happening

The probability of an event \(A\) not happening is \(P(\overline{A})=1 - P(A)\).
Given \(P(A)=\frac{17}{50}\), then \(P(\overline{A}) = 1-\frac{17}{50}=\frac{50 - 17}{50}=\frac{33}{50}\).

Step2: Find the odds in favor of event \(A\)

The formula for odds in favor of an event \(A\) is \(\frac{P(A)}{P(\overline{A})}\).
Substitute \(P(A)=\frac{17}{50}\) and \(P(\overline{A})=\frac{33}{50}\) into the formula: \(\frac{\frac{17}{50}}{\frac{33}{50}}=\frac{17}{33}\), so the odds in favor of event \(A\) are \(17\) to \(33\).

Step3: Find the odds against event \(A\)

The formula for odds against an event \(A\) is \(\frac{P(\overline{A})}{P(A)}\).
Substitute \(P(A)=\frac{17}{50}\) and \(P(\overline{A})=\frac{33}{50}\) into the formula: \(\frac{\frac{33}{50}}{\frac{17}{50}}=\frac{33}{17}\), so the odds against event \(A\) are \(33\) to \(17\).

Answer:

a) \(17\) to \(33\)
b) \(33\) to \(17\)