Last week we explored the statistical probabilities of global destruction and winning the lottery. Let’s now make it a two-parter and talk about something much more commonplace, namely: Will it rain?
This idea came from some recent dinner guests. The conversation turned to the weather. That’s usually a poor reflection on the host. When people talk about the weather, they’re often desperate for some discussion topic. But these folks brought up an interesting issue. You see, the forecast for the next three days went like this: Sunday, 40 percent chance of rain; Sunday night, 40 percent chance of rain; Monday, 40 percent chance of rain.
The guests were all gardeners. It has been a dry summer. Nobody really wanted to spend an hour watering. Everyone wanted rain. The question was: If the Weather Service’s forecasts were accurate, then what were the chances that it would rain sometime in the period? What do you think?
With a 40 percent chance tomorrow, tomorrow night and then again the next day, what are the chances that we’ll get rain any time during that entire period? One person at the table said 40 percent. Another thought it was less than that. Another guessed it might be as much as a coin toss, or 50/50. I did some quick math and revealed the surprising answer: Rain was about 80 percent likely. Everyone was amazed – which means that it’s a good topic for this page.
Here’s how you calculate multiple probabilities: First, you determine the odds that it won’t rain. In this case, it’s 60 percent for each of the three periods in question. So you grab your calculator and punch in 0.6 times 0.6 times 0.6 and this equals 0.216. Bingo: Those are the odds that it will not rain during the entire three periods in question. It’s 21.6 percent. Finally, you subtract this from one to get the chance that it will rain: 78.4 percent. Roughly speaking, there’s an 80 percent chance that it will rain. Amazing, right?
Let’s do another, for practice. Say the Weather Service predicts only a 30 percent chance of rain today, and again tonight and again tomorrow. Now you multiply 0.7 times 0.7 times 0.7, which equals 0.343, which means a 34 percent chance of not raining – thus, a 66 percent chance that it will rain during the period.
If this sounds illogical, consider that 30 percent is roughly a one-in-three chance. Pretend you had three marbles in a bag: one red and two green. You blindly reach in and pull out a marble. What are the odds that you’ll get the red one? It’s one in three, right? But now pretend you get three chances. If you first pull out a green one, you throw it back and get another try, and then a third try. Doesn’t logic tell you that with three chances, you’re likely to succeed?
Similarly, with three chances for rain, even if it’s just a one-in-three probability each time, you’re likely to get wet when the three periods in question have elapsed. So keep those umbrellas (and calculators) handy.