Elements of Chance Exemplar – Card Game

Problem When drawing 3 cards from a hand of 4 red cards and 4 black cards, what is the chances of drawing more red than black cards?

Prediction I predict that the most likely outcomes will either be 2 Red or 1 Red.

Plan To complete a single trial: Start off with 8 cards. 4 black cards and 4 red cards. Shuffle these 8 cards either on the desk or in your hand. Select without looking 3 cards from the pack. Record how many red cards in a table similar to this one: Carry out steps 1 to 4, at least 40 times. 0 Red 1 Red 2 Red 3 Red Tally Total Relative Frequency

Data 0 Red 1 Red 2 Red 3 Red Tally IIIII IIIII IIIII III Total 5 13 16 6 Relative Frequency 5/40 = 0.125 13 / 40 = 0.325 16 / 40 = 0.4 6 / 40 = 0.15

Analysis I notice that the most common outcome was 2 Reds. According to my simulation the probability of 2 Reds was 0.4 I notice that the least likely outcome was no reds. Also all 3 Red had a similar chance of occuring. The shape of the results looks bell shaped with the two middle outcomes (1 Red and 2 Reds) occurring the most often.

Theoretical Probability

Conclusion In conclusion my prediction my simulation and my theoretical calculations were all quite similar. When playing this game it is equally likely that you will get 2 Reds or 1 Red. It is also equally likely that you will get 0 Reds or all 3 Reds. 0 Reds and 3 Reds are less likely than the 2 or 1 Red.

Evaluation