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Commonly Used Formulas in Probability Odds:P(A)1...

Commonly Used Formulas in Probability

Odds:P(A)1 - P(A)

General Law of Addition: P(A ? B) = P(A) + P(B) - P(A n B)

Conditional probability: P(A | B) = P(A n B)P(B)

Independence property: P(A n B) = P(A)P(B)

Bayes’s Theorem: P(B | A) = P(A | B)P(B)

P(A | B)P(B) + P(A | B_)P(B_)

Permutation: n Pr = n!(n - r )!

Combination: nCr = n!r !(n - r )!

5.62 A certain airplane has two independent alternators to provide electrical power. The probability that a given alternator will fail on a 1-hour flight is .02. What is the probability that (a) both will fail? (b) Neither will fail? (c) One or the other will fail? Show all steps carefully.

5.70 The probability is 1 in 4,000,000 that a single auto trip in the United States will result in a fatality. Over a lifetime, an average U.S. driver takes 50,000 trips. (a) What is the probability of a fatal accident over a lifetime? Explain your reasoning carefully. Hint: Assume independent events. Why might the assumption of independence be violated? (b) Why might a driver be tempted not to use a seat belt “just on this trip”?

Odds:P(A)1 - P(A)

General Law of Addition: P(A ? B) = P(A) + P(B) - P(A n B)

Conditional probability: P(A | B) = P(A n B)P(B)

Independence property: P(A n B) = P(A)P(B)

Bayes’s Theorem: P(B | A) = P(A | B)P(B)

P(A | B)P(B) + P(A | B_)P(B_)

Permutation: n Pr = n!(n - r )!

Combination: nCr = n!r !(n - r )!

5.62 A certain airplane has two independent alternators to provide electrical power. The probability that a given alternator will fail on a 1-hour flight is .02. What is the probability that (a) both will fail? (b) Neither will fail? (c) One or the other will fail? Show all steps carefully.

5.70 The probability is 1 in 4,000,000 that a single auto trip in the United States will result in a fatality. Over a lifetime, an average U.S. driver takes 50,000 trips. (a) What is the probability of a fatal accident over a lifetime? Explain your reasoning carefully. Hint: Assume independent events. Why might the assumption of independence be violated? (b) Why might a driver be tempted not to use a seat belt “just on this trip”?

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