Tuesday, July 14, 2009

Numeracy in a Public Service Announcement

The BC gaming commission has produced a new ad for TV aimed at helping the viewer understand the idea of simple probability.
Have a look at it. http://www.bclc.com/documents/GameSense_Conform_bar.wmv

It's funny and I think it attempts to portray the concept that the probability of an event happening (in this case, a girl accepting the guy's advances) as being independent of the number of times you repeat that event.

In the case in this ad, the chances of the girl accepting his advances do not improve despite the number of times he attempts to get her attention.

I see this like a simple probability experiment, much like flipping a coin. The probability of you flipping a specific side (heads or tails) on any given flip does not change, regardless of how many times you flip that coin.

Looking at the situation portrayed in the ad as a probability experiment, the probability of the woman saying yes is one out of two possible outcomes (yes or no).

Expressed mathematically this is:
P(yes) = ½ or 50%

Interestingly, the probability of her saying yes is also 50% for any given attempt.

Hmm... in that case, if this was really like the coin flip experiment it would have had to have been a woman with no short-term memory. In order for this to be a truly random event, she would have had no memory of him having asked her before. As she does have a memory of his advances, this is influencing her response. In this woman's case, her memory will either cement her decision to refuse him or eventually he will wear her down and she will accept. Not random at all.

I realize the point of the Public Service Ad is to hep people realize that repeated play in a casino game is not making the probability of them winning any better, but perhaps the depiction they chose is not the best suited to their message, as the event they are depicting doesn't really convey that message when you start to dissect it.

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