Question

suppose that (a) and (b) are independent events such that (p(a) = 0.10) and (p(overline{b}) = 0.40).

find (p(a cap b)) and (p(a cup b)). (if necessary, consult a list of formulas.)

(a) (p(a cap b) = )
(b) (p(a cup b) = )

Explanation:

Find the probability of event B

Using the Probability of Events knowledge point

$$ P(B) = 1 - P(\overline{B}) = 1 - 0.40 = 0.60 $$

Calculate the intersection probability

Using the Independent Events Probability knowledge point

$$ P(A \cap B) = P(A) \times P(B) = 0.10 \times 0.60 = 0.06 $$

Calculate the union probability

Using the Probability of Events knowledge point

$$ P(A \cup B) = P(A) + P(B) - P(A \cap B) = 0.10 + 0.60 - 0.06 = 0.64 $$

Answer:

Question 1

(a) \(P(A \cap B) =\) <blank>0.06</blank>

Question 2

(b) \(P(A \cup B) =\) <blank>0.64</blank>