Probability: Using "And" with Independent Events

Experiment with independent events: College Year and College Major. Compare simulated proportions to theoretical probabilities, including the probability of Year AND Major.

Directions

Pick a College Year and a College Major. Press Roll now to simulate that many students, independently assigning a Year and a Major according to the probabilities in the tables. The chart shows the proportions for your selected Year, your selected Major, and the event where both occur on the same student (Year AND Major). Press Restart to clear results.

How to play (and the math)

Probability note: For independent events A and B, P(A and B) = P(A) × P(B). Here, A is the selected College Year and B is the selected College Major. During simulation, we draw Year and Major independently using the given distributions. As the number of rolls increases, simulated proportions should approach these theoretical values.

College YearProbability
First.29
Second.27
Third.23
Fourth.21
 Probabilities sum to 1.00.
College MajorProbability
Business.19
Health Professions.13
Social Sciences and History.07
Biological and Biomedical.07
Psychology.06
Other.48
 Probabilities sum to 1.00.

Controls

How many rolls to add?
College Year
College Major
Adds the selected number of simulated students. Clears all results and resets counts to zero. Selections remain as chosen.

Results

Proportions (simulated)
Proportions by Event Three bars show the proportion of the selected Year, the selected Major, and Year AND Major. Y-axis from 0 to 1 with major grid lines at 0.10 and minor at 0.05.

Total rolls: 0. Current proportions — Year (First): 0.0000, Major (Business): 0.0000, and First AND Business: 0.0000

Theoretical: P(Year (First)) = 0.29, P(Major (Business)) = 0.19, P(First AND Business) = 0.29 × 0.19 = 0.0551

EventCountProportion
 Counts and proportions update after each action.