Question 9 (Mandatory) (5 points) Non-mutually exclusive events can occur jointl

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Question 9 (Mandatory) (5 points) Non-mutually exclusive events can occur jointly . Example: In a deck of 52 cards, there are 4 suites (heart, diamond, club, spade), each suite has 4 face cards (ace, king, queen, jack) and 9 number cards (2- 10) If event A is hearts. Adding Place) + Ptheart). we get 4/52 13/52-17/52. but we know there the card drawn is heart and event B is ace, these events can occur jointly as ace of are only 16 cards (13 hearts and 3 more aces) So that PIA and B) is not double counted it must be subtracted from PIA) P(B) General Addition Rule: PA or B) PA)+ P(B) PA and B). Applying the General Addition Rule to the example. Place or hearts) 13/52 4/52-1/52- 16/32 Additional Reading Under Contents, select "Probability of A or B' For the event A or B. where A and B may occur joindly. which rule applies? Select an Option Save Previous Page Next Page Page 9 of 17

Explanation / Answer

For the event A or B, where A and B may occur jointly, then we apply General Multiplication Rule of probability:

General Multiplication Rule: P (A and B)= P(A) X P(B | A)

The multiplication rule, which states that the joint probability of A and B is the product of the conditional probability of B given A, times the probability of A. In probability notation:

  P (A and B)= P(A) X P(B | A)

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