Refresher Course 102: Determining Probability

Posted June 6th, 2016.

Categories: Employment Law, The Calculating Lawyer.

probability mark s guralnick

The probability of a single event happening is the number of desired outcomes divided by the number of possible outcomes. It is the number of ways in which an event can occur divided by the number of possible events. To determine a probability, we start with a fraction. So, for example, if we wished to determine the probability of tossing heads up on a coin toss, the fraction would look like this:

Number of ways in which a coin can land heads up
_______________________________________  =     1/2
Number of possible ways in which the coin can land

The probability of 1/2 can then be converted to a decimal figure (0.5) or a percentage (50%). Thus, there is a 50% probability that by flipping a coin, it will land heads up.

Consider another example: Assume there is a tray of cupcakes, consisting of four chocolate cupcakes and six vanilla cupcakes. Assume also that it is impossible to tell them apart until one bites into them. What is the probability of choosing a chocolate cupcake? A vanilla cupcake? A chocolate or vanilla cupcake?  If you answered 2/5, 3/5 and 1, you would be correct.

THE EQUATIONS:

Probability of choosing chocolate =  Number of chocolate cupcakes / Total number of cupcakes  = 4/10 = 2/5

Probability of choosing vanilla = Number of vanilla cupcakes / Total number of cupcakes       = 6/10 = 3/5

Probability of choosing a chocolate or vanilla cupcake = Number of vanilla cupcakes/ Total number of cupcakes = 10/10 = 1

Another way to express these fractional results is in the form of percentages. In other words, there would be a 40% probability of picking chocolate, a 60% probability of picking vanilla, and a 100% probability of picking one or the other.

Probability calculations are another useful tool that can aid attorneys in making judgments or providing advice. Consider, for example, an employment discrimination case which has been scheduled for a trial by jury. Fifty local citizens have reported to the local courthouse for jury duty, of which 35 are Caucasian, 10 are African American, and 5 are Hispanic. Of the jurors, 18 are under the age of 30; the remainder are 30 or older. Half are male; half are female. Can you quickly calculate the probability of the events listed in the left column below without looking at the answers in the right column below?

           

                 

What is the probability that: Answer
1. The first juror selected from the jury pool will be Hispanic? 10%
2. The first juror selected will be a woman? 50%
3. The first juror selected will be under 30 years old? 36%
4. The first juror selected will be either Hispanic or Caucasian? 80%
5. The second juror selected will be an African American (assuming that the first juror selected from the jury pool was not African American) 20.4%
6. The second juror selected will be an African American (assuming that the first juror selected from the jury pool was African American) 18.37%
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