A telemarketing supervisor tells a new worker that the odds of making a sale on a single call are 4 to 15. What is the probability of a successful call? (Enter your answer to 2 decimal places.)
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To calculate the probability of making a successful call, we can use the odds ratio given to us. The odds ratio is expressed as a ratio of the number of successful outcomes to the number of unsuccessful outcomes.
In this case, the odds of making a sale on a single call are given as 4 to 15. This means that for every 4 successful calls, there are 15 unsuccessful calls.
To calculate the probability, we need to convert the odds ratio into a probability ratio. We can do this by dividing the number of successful outcomes by the total number of outcomes. In this case, the total number of outcomes is the sum of successful and unsuccessful outcomes.
Probability of success = Number of successful outcomes / Total number of outcomes
To calculate the total number of outcomes, we add the number of successful and unsuccessful calls:
Total number of outcomes = Number of successful outcomes + Number of unsuccessful outcomes
Given that the odds of success are 4 to 15, we can assign the following values:
Number of successful outcomes = 4
Number of unsuccessful outcomes = 15
Now let's plug in these values into the formulas:
Total number of outcomes = 4 + 15 = 19
Probability of success = 4 / 19 ≈ 0.21
Therefore, the probability of a successful call is approximately 0.21, or 21% when rounded to two decimal places.