Suppose we put a total of r balls, independently one at a time, in k boxes. Probability that each ball goes into box i is pi, such that ∑i=1 pi = 1. Collision occurs when we put a ball in none empty box. There are 9 collisions if a bin is filled with 10 balls. […]
Suppose you flip a biased coin until two of the most recent three flips are heads. Theprobability that you see a head is p. X is the random variable that denotes the number of total flips. Ifthe first two flips are heads, then X = 2. Find the expected value of X. Looking for […]
Tom is a weatherman in New York. On days when it snows, Tom correctly predicts the snow 70% of the time. When it doesn’t snow, he correctly predicts no snow 95% of the time. In New York, it snows on 10% of all days. Tom’s friend Jerry is a weatherman in Alaska. Jerry claims that […]
Box 1 contains 1000 lightbulbs of which 10% are defective. Box 2 contains 2000 lightbulbs of which 5% are defective. Suppose a box is given to you at random and you randomly select a lightbulb from the box. If that lightbulb is defective, what is the probability you chose Box 1? Looking for a […]
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