Suppose P (E) = 0.15, P (F) = 0.65, and P (F | E) = 0.82, compute the following:

P (E and F). P (E or F). P (E | F).

P (E and F) = 0.123

P (E or F) = 0.677

P (E|F) = 0.189

Step-by-step explanation:

The formula for conditional probability is P (B|A) = P (A and B) / P (A)

The addition rule is P (A or B) = P (A) + P (B) - P (A and B)

∵ P (E) = 0.15

∵ P (F) = 0.65

∵ P (F|E) = 0.82

- Use the first rule above

∵ P (F|E) = P (E and F) / P (E)

- Substitute the values of P (F|E) and P (E) to find P (E and F)

∴ 0.82 = P (E and F) / 0.15

- Multiply both sides by 0.15

∴ 0.123 = P (E and F)

- Switch the two sides

∴ P (E and F) = 0.123

Use the second rule to find P (E or F)

∵ P (E or F) = P (E) + P (F) - P (E and F)

∴ P (E or F) = 0.15 + 0.65 - 0.123

∴ P (E or F) = 0.677

Use the first rule to find P (E|F)

∵ P (E|F) = P (F and E) / P (F)

- P (F and E) is the same with P (E and F)

∴ P (E|F) = 0.123/0.65

∴ P (E|F) = 0.189