Responsible gambling - Consumer Affairs Victoria

CONTINUED
A2
What are my chances?
Exercise 2 - Probability
Probability aims to express chance mathematically.
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Responsible Gambling | Section A: What’s the big deal?
Consumer Affairs Victoria | consumer.vic.gov.au
Assuming you toss a fair coin, there is the same chance of it landing heads as there is of it
landing tails. In other words there is a 50/50 chance of heads (and a 50/50 chance of tails) or
50% or 1/2.
Another way of thinking of this is that probability compares the number of ways a desired
outcome can happen to the number of possible outcomes overall:
Number of successful outcomes
Probability of a particular event = –––––––––––––––––––––––––––––
Number of possible outcomes
So for example, the chance of getting a successful outcome of heads with tossing a coin is 1
(the only successful outcome) over 2 (as there are 2 possible results; heads or tails) = ½ or 0.5
The outcome of tossing a fair coin is random. There is no way to tell whether it will be heads
or tails based on past events.
Look at the pattern on heads and tails in the data for Exercise 1. Were there any consecutive
runs of heads or tails?
If so, when tossing the coins, did you think that the other side must be due to come up?
Many people would, and this is the gamblers’ fallacy. Random numbers can result in patterns.
When they do occur, it is coincidence. Random numbers are not dependent on previous
numbers and so patterns are just as likely as no patterns.
The probability of 0.5 refers to each coin toss. Each toss starts fresh and the coin has no
memory of what has just happened. And the 50% chance is just a chance. There is also an
equal chance it could go the other way and this is true for every throw.
Note that a random set of numbers does not necessarily mean that runs of consecutive
numbers or repeated patterns will not appear.
a) Place the chance of the following occurrences happening on the probability line.
0 1
No chance certain
A Heads on a single toss (H)
A Tails on a single toss (T)
Drawing a red card from a single pack of cards (no Jokers) (R)
Drawing an ace from a single pack of cards (no Jokers) (A)
Drawing a spade from a single pack of cards (no Jokers) (S)
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