Answer:
P(E and F) = 0.123
P(E or F) = 0.677
P(E|F) = 0.189
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