If A and B are events with P(A) = 3/8, P(B) = 1/2 and P(A∩B) = 1/4. Find $$P(\overline{A} \cap \overline{B})$$​

Correct option is B

Given:
P(A) = 3/8, P(B) = 1/2, P(A ∩ B) = 1/4
Formula Used:
We can use the complement rule for this probability problem. The complement of an event A is the event that A does not occur.
The formula to find $$P(\overline{A} \cap \overline{B})$$​is given by the complement of the union of A and B:
​$$P(\overline{A} \cap \overline{B}) = 1 - P(A \cup B)$$​​
Also, P(A ∪ B) can be found using the formula:
P(A ∪ B) = P(A) + P(B) - P(A ∩ B)
Solution:
P(A ∪ B) = P(A) + P(B) - P(A ∩ B)
P(A ∪ B) = 3/8 + 1/2 – 1/4
P(A ∪ B) = 3/8 + 4/8 - 2/8 = 5/8
$$P(\overline{A} \cap \overline{B})$$​ = 1 - P(A ∪ B)
​$$P(\overline{A} \cap \overline{B})$$​= 1 - 5/8 = 3/8
Therefore, $$P(\overline{A} \cap \overline{B})$$​ is 3/8.