Verify that this is a probability model. B.) Use Benford’s Law to determine the probability that a randomly selected first digit is 1 or 2. C.) Use Benford’s Law to determine the probability that a randomly selected first digit is at least 6.
1. In 1881, Simon Newcomb discovered that digits do not occur with equal frequency. After studying lots of data, he assigned probabilities for each of the first digits of numbers. This is known as Benford’s Law (because a physicist named Frank Benford proved it at a later date) and plays a major role in identifying tax fraud.
Digit Probability
1 0.301
2 0.176
3 0.125
4 0.097
5 0.079
6 0.067
7 0.058
8 0.051
9 0.046
A.) Verify that this is a probability model.
B.) Use Benford’s Law to determine the probability that a randomly selected first digit is 1 or 2.
C.) Use Benford’s Law to determine the probability that a randomly selected first digit is at least 6.
2. Suppose that a single card is selected from a standard 52-card deck.
A.) Compute the probability of the event E = “drawing a king.”
B.) Compute the probability of the event E = “drawing a king” or F = “drawing a queen” or G = “drawing a jack.”
3. Suppose that a pair of dice are thrown. Let A = “the first die is a 3”, let B = “the sum of the dice is less than or equal to 6”, let C = "the sum of the dice is 9", and let D = "the second die is a 5. Find the following:
a.) P(A or D)
b.) P(A and B)
c.) P(A or B or D)
d.) P[A or B or C)]
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