Probability Investigation
PROBLEM
I wonder how likely it is that I can draw 3 red cards from my pack of 10 cards. I expect it won't happen very much, perhaps it might happen once or twice in 50 trials.
PLAN
I have 10 cards in my pack, 4 red and 5 green and 1 blue. I will shuffle the cards face down and turn up three cards at random. I will record the results in a table. I will then return the cards to the pack and reshuffle them. I will repeat this process 50 times. I will use the data to draw a bar chart. The possible outcomes are:
0 red cards
1 red card
2 red cards
3 red cards
0 red cards
1 red card
2 red cards
3 red cards
DATA in a frequency table
ANALYSIS
I notice that the most frequent result was getting 1 red card which was 44% of the time followed by 0 red cards 30% of the time. I got 2 red cards 22% of the time and 3 red cards only 4% of the time. The graph is skewed to the right because getting no red cards and 1 red card happen more often than getting 2 red cards and 3 red cards.
CONCLUSION
From my results I see that I got 3 red cards the least amount of times at 4%.
I conclude that in the long run I am most likely to get 1 red card, then the next most likely is to have no red cards, followed by 2 red cards and the least likely is to have all three red cards.
Overall, I expect to get 1 red card the most if I was to repeat the experiment.
I conclude that in the long run I am most likely to get 1 red card, then the next most likely is to have no red cards, followed by 2 red cards and the least likely is to have all three red cards.
Overall, I expect to get 1 red card the most if I was to repeat the experiment.
end of report
To answer my question I got 3 red cards 2 times out of 50 which is 4%. My experiment shows me I am more likely to get 1 red card as an outcome than any other. Out of 50 trials this happened 44% of the time. However, choosing no red cards happened 30% of the time followed by 2 red cards which happened 22% and least likely was getting 3 red cards on 4%. This was no surprise as I didn't expect to get 3 red cards a lot in this experiment.
According to theoretical probability the chance of getting 3 red cards is 4/10 x 3/9 x 2/8 = 24/720 or 3.3%. This also means that the probability of not getting 3 red cards is 96.7% (1 - 0.033 = 0.967). I got it two times out of 50 (4%) which is only a difference of 0.7%. However, I have only conducted 50 trials. This is quite a small sample size. If I repeated this experiment again with 50 trials I expect I would get similar results because my sample size is the same. Based on my experiment I would expect to get 3 red cards twice in another trail. However, I also suspect that if I conducted much larger trials, say 1000 or even larger, in the long run I would get results that approach the theoretical value of 3.3%.
Another reason why I didn't get a result close to the theoretical result might be the way I shuffle the cards on my desk. Perhaps I didn't shuffle them enough and that's why I selected slightly more red cards than expected.
According to theoretical probability the chance of getting 3 red cards is 4/10 x 3/9 x 2/8 = 24/720 or 3.3%. This also means that the probability of not getting 3 red cards is 96.7% (1 - 0.033 = 0.967). I got it two times out of 50 (4%) which is only a difference of 0.7%. However, I have only conducted 50 trials. This is quite a small sample size. If I repeated this experiment again with 50 trials I expect I would get similar results because my sample size is the same. Based on my experiment I would expect to get 3 red cards twice in another trail. However, I also suspect that if I conducted much larger trials, say 1000 or even larger, in the long run I would get results that approach the theoretical value of 3.3%.
Another reason why I didn't get a result close to the theoretical result might be the way I shuffle the cards on my desk. Perhaps I didn't shuffle them enough and that's why I selected slightly more red cards than expected.