There are three types of coins which have different probabilities of landing heads when tossed.
- Type A coins are fair, with probability .5 of heads
- Type B coins are bent and have probability .6 of heads
- Type C coins are bent and have probability .9 of heads
Suppose I have a drawer containing 4 coins: 2 of type A ,1 of type B ,and 1 of type C .I reach into the drawer and pick a coin at random. Without showing you the coin I flip it once and get heads. What is the probability it is type A? Type B? Type C?
You're about to get on a plane to Seattle. You want to know if you should bring an umbrella. You call 3 random friends of yours who live there and ask each independently if it's raining. Each of your friends has a 2/3 chance of telling you the truth and a 1/3 chance of messing with you by lying. All 3 friends tell you that "Yes" it is raining. What is the probability that it's actually raining in Seattle?
You test two types of buttons on your website, version A and B. For version A, out of 100 visitors, 4 converted. For version B, 6 converted. Is version B better?
- https://www.peakconversion.com/2012/02/ab-split-test-graphical-calculator/
- http://getdatadriven.com/ab-significance-test
You are a statistician during WWII. Tanks from the enemy camp were captured. Assume they are a random sample from all tanks produced. Assume you're on the allies side.
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Suppose 1 tank with serial number 130 is captured. How many tanks do you think were captured?
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Suppose 4 tanks with serial numbers 19, 40, 42 and 60 are captured. How many tanks where produced?