Ace of Hearts means both events happen together Venn Diagram showing non- mutually exclusive events: When events A and B are mutually exclusive: P(B)
FSMQ Laws of probabiilty
can be any value between 0 and 0 70 d cannot be determined with the information given 2 The intersection of events A and B is the event that occurs when:
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Events are mutually exclusive if they cannot co-occur For example, a flipped coin can come up heads or tails, but not both Therefore, the possible outcomes of a
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B ⊆ Ω The conditional probability of event B, given event A, is P(B A) = P(B ∩ A ) Definition: Events A and B are mutually exclusive, or disjoint, if A ∩ B = ∅
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For instance, if E is an event, then E and its complement not E are mutually exclusive, A and B are mutually exclusive, since one experiment produces but one
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events The previous example suggests a rule for working out the probability of either of two mutually exclusive events happening: If A B are mutually exclusive
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If A and B are mutually exclusive, what is P(A and B)? Are the events “Julie draws a beer on the first draw” and “Julie draws a beer on the second draw”
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Statistics; Sec 5.2b - Some Probability Rules (Addition) If A and B are mutually exclusive events compute P(A or B). P(A or B) = P(A) + P(B).
If A and B are mutually exclusive events with P(A)=0.6 and P(B)=0.3 find the following: (a) P(A U B) (b) P(A n B) (c) P(A U B ) (d) P(A
B ? ?. The conditional probability of event B given event A
Ace of Hearts means both events happen together. Venn Diagram showing non- mutually exclusive events: When events A and B are mutually exclusive: P(B).
can be any value between 0 and 0.70. d. cannot be determined with the information given. 2 The intersection of events A and B is the event that occurs when:.
2.4 The Partition Theorem (Law of Total Probability). Definition: Events A and B are mutually exclusive or disjoint
Important to distinguish independence from mutually exclusive which would say B ? A is empty (cannot happen). Example. Deal 2 cards from deck. A first card is
The probability of the complement of A is: ______. Enter your answer to three decimal places. 8. answer: source: objective: 8 If the events A and B are
When we draw cards from a deck the four suits are mutually exclusive. A drawn card can be a heart
Three events A B and C are said to be mutually independent if all the If E1
If A andB aremutually exclusive thenP(A ) =P(A) +P(B) P(A B) Conditional probability: P(AjB) = P(B) Multiplication rule: P(A ) =P(AjB)P(B) =P(BjA)P(A) The Partition Theorem: if B1B2 B form a partitionof ? then m P(A) =X P(A i=1 As a special case B Bi) =XP(AjBi)P(Bi) i=1 andB partition ? so: for any event A P(A) == P(A B) +P(A B)
1 The Complement Rule Because Aand Ac are mutually exclusive P(A) + P(Ac) = P(A[Ac) = P() = 1 or P(Ac) = 1 P(A): Toss a coin 4 times Pffewer than 3 headsg= 1 Pfat least 3 headsg= 1 5 16 = 11 16: We can extend this If AˆB then the P(BnA) = P(B) P(A) 2 The Inclusion-Exclusion Rule For any two events Aand B P(A[B) = P(A) + P(B) P(AB)
Events A and B are independent if probability of A given B equals probability of A Dependent events (or non-independent events): Events that are not independent i e P(A given B) ? P(A) Mutually exclusive events (or disjoint events): If event A occurs then event B cannot occur and conversely
Mutually exclusive and B are mutually exclusive Find the missing probability 15) P(A) = Find the missing probability 17) P(A) = 18) P(not A) = = ? 16) P(A) = Create your own worksheets like this one with Infinite Precalculus Free trial available at KutaSoftware com
Two events are independent if and only if the probability of one event (A) occurring is not affected by whether the other event (B) occurs or not Events A and B are independent if P(A) = P(AB) knowing that B occurs does not change the probability of A occurring P(event) = P (event condition)
Mutually exclusive Events A and B are mutually exclusive Find the missing probability 15) P(A) = = ? 16) P(A) = Find the missing probability 17) P(A) = 18) P(A) = Create your own worksheets like this one with Infinite Algebra 2 Free trial available at KutaSoftware com Worksheet
Can two events be exhaustive and independent simultaneously?
Yes, events are exhaustive and independent. Suppose two events A and B are exhaustive, i.e. A ? B = S are also can be independent if and only if P(A ? B) = P(A) P(B).
Are two disjoint events always complementary?
Yes, complementary events are always mutually exclusive. This means that an event and its complement will not share any outcomes. Are Complementary Events Disjoint? Disjoint events are events that cannot occur at the same time. In other words, they are mutually exclusive. Thus, complementary events are disjoint.
When are two events independent?
You can tell that two events A and B are independent if the following equation is true: P (AnB) = P (A)P (B) where P (AnB) is the probability of A and B occurring at the same time. This is called the multiplication rule for independent events. We can also express the idea of independent events using conditional probabilities .
What are two independent events?
Two events are independent if the outcome of one event does not affect the likelihood of the other event. Let A and B be independent events. Then the probability of A and B occurring is: Two coins are tossed. Find the probability of the following event.
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