Non-mutually exclusive events can occur jointly. Example: in a deck of 52 cards,

Question

Non-mutually exclusive events can occur jointly. Example: in a deck of 52 cards, there are 4 suites (heart, diamond, club, spade), each suite has4face cards (ace, king, queen, jack) and 9 number cards (2-10). If event A is the card drawn is heart and event B is ace, these events can occur jointly. Adding P(ace) +P(heart), we get=4/52 + 13/52 = 17/52, but we know there are only 16 cards (13 hearts and 3 more acres). So that P(A and B) is not double counted, P(A or B) = P(A) + P(B) - P(A and B), which is the General Addition Rule. So, P(A or B) = 13/52 + 4/52 -1/52 = 16/32 P(A) = 0.412 P(B) = 0.117 P(C) = 0.487 P(A and B)= 0.016 If P(A and B) = 0, A and B are mutually exclusive. Otherwise, A and B can occur jointly Which applies? Simple Multiplication Rule: P(A and B) = P(A)*P(B) Simple Addition Rule: P(A or B) = P(A) + P(B) General Addition Rule: P(A or B) = P(A) + P(B) - P(A and B) P(A or B) = P(A or B or C) =

Explanation / Answer

18) When A and B are jointly distributed then P(A and B) not 0.

i.e. General Addition Rule: P(A or B) = P(A) +P(B) -P( A and B)

When A and B are mutually exclusive then P(A and B) = 0

i.e. Simple Addition rule: P(A or B) = P(A) + P(B)

19) Consider,

P(A or B) = P(A) +P(B) - P(A and B)

= 0.412 + 0.117 - 0.016

= 0.513

20) Consider,

P(A or B) = P(A) + P(B) + P(C) - P(A and B) - P(A and C) - P(B and C) + P(A and B and C)

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