43 Probability intuition
The following two activities will test your probability intuition and ability to justify your probability estimate.
You might find it useful to use a tree diagram or other theoretical calculations to support the result you obtained through simulation.
Think about whether there is a difference between your intuition (what you expect to happen) and your probability estimate? Is there anything else that needs to be taken into account?
Trick cards
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In a game of chance there are three cards:
The dealer shuffles the cards and shows you a card-back. What is the probability that the other side is the 4 of hearts? |
You can use the following Scratch program to get a feel for how the game works.
1. Play the game at least 10 times and note the number of times a card-back was shown at first, and then out of those, how many times the other side was a card back.
2. Can you draw a tree diagram illustrating what is happening as the card is drawn and then flipped over?
Disorderly plane seating
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A plane has its tickets organised so that the first person in line sits in seat 1, the second person in line in seat 2, and so on.
However today the first person in line is crazy, and so chooses a random seat. If everyone following him sits in their assigned seat if it’s empty, or a random seat if it’s not, what are the odds the last passenger can sit in his or her correct seat? |
1. Try the program out at least 10 times, and note the number of times the last person got to sit in the last seat.
2. Can you draw a tree diagram illustrating what happens? Try it for the case of just 3 passengers.
Creating a computer simulation for the trick card problem (simulating sequential events)
In the card trick problem, the dealer first draws a card and then shows a random side. The outcome of the first event (drawing a card) alters the probability of outcomes for the sequential events. We already know how to model such situations using tree diagrams, and that will be an important strategy when it comes to looking at the theoretical probability. However, it’s also useful to model these scenarios using a simulation so that we can investigate and test our theoretical calculations. A simulation can also give us an intuitive feel for what happens.
The following video goes through setting up a simulation of the card-trick problem in Scratch.
You can see the code at the project page. Note that you could have a different structure or slightly different probabilities.
