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Chapter 8: Problem 32

The odds in favor of an event \(E\) occurring are 9 to 7 . What is the probability of \(E\) occurring?

Short Answer

Expert verified
The probability of \(E\) occurring is \(\frac{9}{16}\).

Step by step solution

01

Identify the favorable and unfavorable outcomes

The favorable outcomes are the chances of the event \(E\) occurring (9) and the unfavorable outcomes are the chances of the event \(E\) not occurring (7).
02

Calculate the total possible outcomes

The total possible outcomes are the sum of the favorable and unfavorable outcomes. In this case, the total possible outcomes are 9 + 7 = 16.
03

Calculate the probability of \(E\) occurring

The probability of event \(E\) occurring can be found by dividing the number of favorable outcomes by the total number of possible outcomes. Therefore, the probability of \(E\) occurring is: \( P(E) = \frac{\text{favorable outcomes}}{\text{total possible outcomes}} = \frac{9}{16} \) So, the probability of event \(E\) occurring is \(\frac{9}{16}\).

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Most popular questions from this chapter

A probability distribution has a mean of 42 and a standard deviation of 2 . Use Chebychev's inequality to find a bound on the probability that an outcome of the experiment lies between a. 38 and 46 . b. 32 and 52 .

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The frequency distribution of the hourly wage rates (in dollars) among blue- collar workers in a certain factory is given in the following table. Find the mean (or average) wage rate, the mode, and the median wage rate of these workers. \begin{tabular}{ccccccc} \hline Wage Rate & \(10.70\) & \(10.80\) & \(10.90\) & \(11.00\) & \(11.10\) & \(11.20\) \\\ \hline Frequency & 60 & 90 & 75 & 120 & 60 & 45 \\ \hline \end{tabular}
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