Given the following: P (A) = 0.3 P (B) = 0.2 P (A OR B) = 0.5 P (A AND B) = 0 Which of the following is true? a. A and B are disjoint. b. A and B are neither disjoint nor independent. c. A and B are independent. d. A and B are disjoint and independent.

Question

Mathematics

Mclean

31 December, 19:49

Given the following: P (A) = 0.3 P (B) = 0.2 P (A OR B) = 0.5 P (A AND B) = 0 Which of the following is true? a. A and B are disjoint. b. A and B are neither disjoint nor independent. c. A and B are independent. d. A and B are disjoint and independent.

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Answers (1)

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Payton Blake · Answer 1

a. A and B are disjoint

Step-by-step explanation:

We know that P (A and B) = 0, It means that event A and event B have nothing in common and it means that event A and event B are disjoints events.

The event A and event B are independent if

P (A and B) = P (A) * P (B)

P (A) * P (B) = 0.3*0.2=0.06

So, P (A and B) ≠P (A) * P (B)

Hence events A and B are not independent.

Option a is A and B are disjoints which is correct

Option b is A and B are neither disjoints nor independent which is partially false as A and B are disjoints event.

Option c states that A and B are independent which is clearly false.

Option d states that A and B are disjoints and independent which is partially false as A and B are not independent.

Hence the correct option is option A.