a. P(A | Bc) can be calculated using the formula:
P(A | Bc) = P(A ∩ Bc) / P(Bc)
Given that P(A ∩ Bc) = 0.03 and P(Bc) = 1 - P(B) = 1 - 0.36 = 0.64, we can substitute these values into the formula:
P(A | Bc) = 0.03 / 0.64 ≈ 0.0469
Therefore, P(A | Bc) ≈ 0.05 (rounded to 2 decimal places).
b. P(Bc | A) can be calculated using the formula:
P(Bc | A) = P(A ∩ Bc) / P(A)
Given that P(A ∩ Bc) = 0.03 and P(A) = 1 - P(Ac) = 1 - 0.57 = 0.43, we can substitute these values into the formula:
P(Bc | A) = 0.03 / 0.43 ≈ 0.0698
Therefore, P(Bc | A) ≈ 0.070 (rounded to 3 decimal places).
c. A and B are independent events if and only if P(A | Bc) = P(A).
From the calculations above:
P(A | Bc) ≈ 0.05
P(A) = 0.43
Since P(A | Bc) ≠ P(A), we can conclude that A and B are not independent events.
The answer is: No because P(A | Bc) ≠ P(A).
Consider the following probabilities: P(Ac) = 0.57, P(B) = 0.36, and P(A ∩ Bc) = 0.03.
a. Find P(A | Bc). (Do not round intermediate calculations. Round your answer to 2 decimal places.)
b. Find P(Bc | A). (Do not round intermediate calculations. Round your answer to 3 decimal places.)
c. Are A and B independent events?
multiple choice
Yes because P(A | Bc) = P(A).
Yes because P(A ∩ Bc) ≠ 0.
No because P(A | Bc) ≠ P(A).
No because P(A ∩ Bc) ≠ 0.
1 answer