Question

An experiment with three outcomes has been repeated 50 times, and it was learned that E₁ occurred 20 times, E₂ occurred 14 times, and E₃ occurred 16 times. Assign probabilities to the following outcomes for E₁, E₂ and E₃. Round your answer to two decimal places.What method did you use?

a)classical method
b)relative frequency method
c)subjective method

Answer 1

To assign probabilities to the outcomes E₁, E₂, and E₃, we will use the relative frequency method. The probabilities for E₁, E₂, and E₃ are 0.40, 0.28, and 0.32 respectively.

Step-by-step explanation:

To assign probabilities to the outcomes E₁, E₂, and E₃, we will use the relative frequency method. The relative frequency of an outcome is the ratio of the number of times the outcome occurred to the total number of trials. In this case, E₁ occurred 20 times out of 50 trials, E₂ occurred 14 times out of 50 trials, and E₃ occurred 16 times out of 50 trials.

The probability of an outcome is the relative frequency of that outcome over the long term. So, to assign probabilities to the outcomes, we divide the number of times each outcome occurred by the total number of trials. Therefore, the probabilities for E₁, E₂, and E₃ are:

E₁: 20 / 50 = 0.40

E₂: 14 / 50 = 0.28

E₃: 16 / 50 = 0.32