Question

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

Explanation:

Step1: Find 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: Calculate the odds in favor of event \(A\)

The odds in favor of an event \(A\) is given by the ratio \(\frac{P(A)}{P(\overline{A})}\).
\(\frac{P(A)}{P(\overline{A})}=\frac{\frac{17}{50}}{\frac{33}{50}}=\frac{17}{33}\), so the odds in favor of event \(A\) is \(17\) to \(33\).

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

The odds against an event \(A\) is given by the ratio \(\frac{P(\overline{A})}{P(A)}\).
\(\frac{P(\overline{A})}{P(A)}=\frac{\frac{33}{50}}{\frac{17}{50}}=\frac{33}{17}\), so the odds against event \(A\) is \(33\) to \(17\).

Answer:

a) \(33\)
b) \(33\)