It is often difficult to distinguish between the probability of an intersection

ID: 3050908 • Letter: I

Question

It is often difficult to distinguish between the probability of an intersection of outcomes (joint probability) and the probability of a conditional outcome (conditional probability). In each case, (i) write down the probability statement; for example, P(Crash Landing | Out of Fuel) or P(Dow Jones Up and Stock Price Up), and (ii) classify it as a joint probability statement or a conditional probability statement. a. Twelve percent of the projects are on time and under budget. b. Of the rivers that are polluted, 80% were within 10 miles of the city. c. Given climate change, hurricanes are likely to become more intense. d. There is a 50% chance that a beam with a weld defect will fail. e. Most beams made in that factory are strong and ductile. It is often difficult to distinguish between the probability of an intersection of outcomes (joint probability) and the probability of a conditional outcome (conditional probability). In each case, (i) write down the probability statement; for example, P(Crash Landing | Out of Fuel) or P(Dow Jones Up and Stock Price Up), and (ii) classify it as a joint probability statement or a conditional probability statement. a. Twelve percent of the projects are on time and under budget. b. Of the rivers that are polluted, 80% were within 10 miles of the city. c. Given climate change, hurricanes are likely to become more intense. d. There is a 50% chance that a beam with a weld defect will fail. e. Most beams made in that factory are strong and ductile. It is often difficult to distinguish between the probability of an intersection of outcomes (joint probability) and the probability of a conditional outcome (conditional probability). In each case, (i) write down the probability statement; for example, P(Crash Landing | Out of Fuel) or P(Dow Jones Up and Stock Price Up), and (ii) classify it as a joint probability statement or a conditional probability statement. a. Twelve percent of the projects are on time and under budget. b. Of the rivers that are polluted, 80% were within 10 miles of the city. c. Given climate change, hurricanes are likely to become more intense. d. There is a 50% chance that a beam with a weld defect will fail. e. Most beams made in that factory are strong and ductile.

Explanation / Answer

a) P(Twelve percent of the projects are on time and are under budget) . It is a joint probability statement.

b)P(Within 10 miles of the city | the rivers are polluted) =0.80

It is aconditional probability statement.

c)P(hurricanes are more intense| climate change true)

It is conditional statement

d) P(Beam with a weld defect will fail) =0.5

It is a joint probability statement

e) P(Beams are strong and ductile |they are made in that factory )

It js a conditional probability statement

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It is often difficult to distinguish between the probability of an intersection

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