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

idk sry

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