Ctrl+k

Conduct simple probability experiments

Simple probability experiments involve identifying possible outcomes, determining whether outcomes are equally likely, and expressing the likelihood of an event as a fraction between 0 and 1. Repeated trials produce experimental probabilities based on observed frequencies, which may vary in small samples but generally become closer to theoretical probabilities as trials increase; conditional probability, dependent events, and formal statistical inference are not included.

Detailed Explanation: Conduct simple probability experiments

To conduct a simple probability experiment:

  1. List all the possible outcomes.
  2. Decide whether the outcomes are equally likely.
  3. Describe the event you are studying.
  4. Find the theoretical probability:
Probability=number of favorable outcomestotal number of equally likely outcomes\text{Probability}=\frac{\text{number of favorable outcomes}}{\text{total number of equally likely outcomes}}
  1. Repeat the experiment and use the results to find the experimental probability:
Experimental probability=number of times the event occursnumber of trials\text{Experimental probability}=\frac{\text{number of times the event occurs}}{\text{number of trials}}

Example: Rolling a fair number cube

Suppose you want to find the probability of rolling an even number.

Step 1: List the possible outcomes.

A number cube can land on:

1,2,3,4,5,61,2,3,4,5,6

Step 2: Check whether the outcomes are equally likely.

Because the number cube is fair, each number has the same chance of being rolled.

Step 3: Identify the favorable outcomes.

The even numbers are:

2,4,62,4,6

There are 33 favorable outcomes out of 66 total outcomes.

Step 4: Find the theoretical probability.

P(even)=36=12P(\text{even})=\frac{3}{6}=\frac{1}{2}

So, the theoretical probability of rolling an even number is 12\frac{1}{2}.

Step 5: Try the experiment.

Roll the number cube 1212 times. Suppose the results are:

3,6,1,4,2,5,6,3,1,2,4,63, 6, 1, 4, 2, 5, 6, 3, 1, 2, 4, 6

The even numbers occur 77 times.

The experimental probability is:

712\frac{7}{12}

The experimental probability, 712\frac{7}{12}, is close to the theoretical probability, 12\frac{1}{2}. They do not have to be exactly the same because a small number of rolls can have unusual results. If you roll the cube many more times, the experimental probability will generally get closer to 12\frac{1}{2}.

Learn by doing: Conduct simple probability experiments

Click a topic below to practice the foundational skills you'll need, learn the steps, or master this skill

    Practice with unlimited practice problems

    Probability - Dice (1), All Specific, To Fraction

      ?