success and failure. Probability experim Making an informed decision Should we convict? A woman who was shopping in Los Angeles had her purse stolen by a young, blonde female who was wearing a ponytail. The blonde female got into a yellow car that was driven by a man with a mustache and a beard. The police located a blonde female named Janet who wore her hair in a ponytail and had a male friend who had a mustache and beard and also drove a yellow car. Based on this evidence the police arrested the two suspects. Because there were no eyewitnesses and no real evidence, the prosecution used probability to make its case against the defendants. The probabilities listed below were presented by the prosecution for the known characteristics of the thieves. Probability 1/10 Characteristic Yellow car Man with mustache 1/4 Woman with ponytail 1/10 Woman with blonde hair 1/3 Man with beard 1/10 Interracial couple in a car 1/1000 (a) Assuming that the characteristics listed above are independent of each other, what is the probability that a randomly selected couple has all these characteristics? That is what is, calculate the probability: P( "yellow car" and "man w/ mustache, beard and .. "interracial couple in car")? (b) Based on the above result would you convict the defendant? Explain thoroughly.

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Permutations and Combinations

If there are 5 dishes, they can be relished in any order at a time. In permutation, it should be in a particular order. In combination, the order does not matter. Take 3 letters a, b, and c. The possible ways of pairing any two letters are ab, bc, ac, ba, cb and ca. It is in a particular order. So, this can be called the permutation of a, b, and c. But if the order does not matter then ab is the same as ba. Similarly, bc is the same as cb and ac is the same as ca. Here the list has ab, bc, and ac alone. This can be called the combination of a, b, and c.

Counting Theory

The fundamental counting principle is a rule that is used to count the total number of possible outcomes in a given situation.