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Teachers & SchoolsStatistics, Data, and Probability I: Drill Set 5, Problem 4. What is the probability that the pointer creates a new winner?

CAHSEE Math | Statistics, Data, and Probability I |

Language | English Language |

Statistics and Probability | Probability |

Statistics, Data Analysis, and Probability 6 | Probability |

What is the probability that the pointer creates a new... winner?

And here are the potential answers...

OK, that FAIR spinner thing again.

For these kinds of problems, FAIR just means that what you see is what you get...

...that is, the drawing is drawn to scale and the spinner isn't a Las Vegas scam to

cheat widows out of their savings by always landing on LOSE.

It's an odds or probability question -- but it's kind of a trick question as well.

Just look at the wheel. The total real estate taken up by "WIN" is ... large.

Like... "clearly over half" large.

Now look at the answers. Anything, uh.. stand out?

Yeah -- it's D.

No other answer could POSSIBLY work. It's D. We can just click it and move on.

Go ahead. Don't be shy. There's nothing wrong with using common sense.

BUT let's assume for a second that we actually want to learn how to solve this problem...

If we really wanted to get fancy, there's a few big fat clues here,

the biggest of which is the presence of right angle.

We know that a right angle is 90 degrees and

is a quarter of a circle... or 25% of it.

And that right angle is bisected with this line. That is, it's cut in half.

So each of these tiny slices is 12.5% of the circle or 45 degrees.

We have 3 LOSES of 12.5% which total to 37.5%.

The wins then have to be 100-37.5% or 62.5%.

We made the calculation but... we really didn't have to.

In fact, wasting so much time makes us feel like a real loser.

Wait a minute...