Mutually Exclusive Events - AP Statistics
Card 1 of 30
For mutually exclusive events $A$ and $B$, $P(A) = 0.4$. Find $P(B)$ if $P(A \text{ or } B) = 0.7$.
For mutually exclusive events $A$ and $B$, $P(A) = 0.4$. Find $P(B)$ if $P(A \text{ or } B) = 0.7$.
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$P(B) = 0.3$. Use $P(A \text{ or } B) = P(A) + P(B)$ and solve.
$P(B) = 0.3$. Use $P(A \text{ or } B) = P(A) + P(B)$ and solve.
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What does it mean for two events to be mutually exclusive?
What does it mean for two events to be mutually exclusive?
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Two events cannot occur simultaneously. Events have no overlap in their outcomes.
Two events cannot occur simultaneously. Events have no overlap in their outcomes.
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State the formula for the probability of mutually exclusive events.
State the formula for the probability of mutually exclusive events.
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$P(A \text{ or } B) = P(A) + P(B)$. No intersection term since $P(A \text{ and } B) = 0$.
$P(A \text{ or } B) = P(A) + P(B)$. No intersection term since $P(A \text{ and } B) = 0$.
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Identify whether these events are mutually exclusive: rolling a 3 or 4 on a die.
Identify whether these events are mutually exclusive: rolling a 3 or 4 on a die.
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Yes, they are mutually exclusive. Each outcome is distinct with no overlap.
Yes, they are mutually exclusive. Each outcome is distinct with no overlap.
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What is the probability of the union of two mutually exclusive events?
What is the probability of the union of two mutually exclusive events?
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The sum of their individual probabilities. Since they cannot occur together, probabilities add directly.
The sum of their individual probabilities. Since they cannot occur together, probabilities add directly.
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If $P(A) = 0.3$ and $P(B) = 0.5$, and $A$ and $B$ are mutually exclusive, find $P(A \text{ or } B)$.
If $P(A) = 0.3$ and $P(B) = 0.5$, and $A$ and $B$ are mutually exclusive, find $P(A \text{ or } B)$.
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$P(A \text{ or } B) = 0.8$. Add probabilities: $0.3 + 0.5 = 0.8$.
$P(A \text{ or } B) = 0.8$. Add probabilities: $0.3 + 0.5 = 0.8$.
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Find $P(A \text{ and } B)$ for mutually exclusive events $A$ and $B$.
Find $P(A \text{ and } B)$ for mutually exclusive events $A$ and $B$.
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$P(A \text{ and } B) = 0$. Mutually exclusive events have no intersection.
$P(A \text{ and } B) = 0$. Mutually exclusive events have no intersection.
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Can mutually exclusive events be independent? Yes or No.
Can mutually exclusive events be independent? Yes or No.
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No. If one occurs, the other has zero probability.
No. If one occurs, the other has zero probability.
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What is another term for mutually exclusive events?
What is another term for mutually exclusive events?
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Disjoint events. Alternative terminology for the same concept.
Disjoint events. Alternative terminology for the same concept.
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If events $A$ and $B$ are mutually exclusive, what is $P(A \text{ and } B)$?
If events $A$ and $B$ are mutually exclusive, what is $P(A \text{ and } B)$?
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$P(A \text{ and } B) = 0$. Defining characteristic of mutual exclusivity.
$P(A \text{ and } B) = 0$. Defining characteristic of mutual exclusivity.
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Determine if these events are mutually exclusive: drawing a heart or a club from a deck.
Determine if these events are mutually exclusive: drawing a heart or a club from a deck.
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Yes, they are mutually exclusive. Different suits cannot overlap on one card.
Yes, they are mutually exclusive. Different suits cannot overlap on one card.
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What happens to the probability of mutually exclusive events occurring together?
What happens to the probability of mutually exclusive events occurring together?
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Probability is zero. By definition, they cannot occur together.
Probability is zero. By definition, they cannot occur together.
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If $A$ and $B$ are mutually exclusive with $P(A)=0.2$ and $P(B)=0.6$, find $P(A \text{ or } B)$.
If $A$ and $B$ are mutually exclusive with $P(A)=0.2$ and $P(B)=0.6$, find $P(A \text{ or } B)$.
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$P(A \text{ or } B) = 0.8$. Add probabilities: $0.2 + 0.6 = 0.8$.
$P(A \text{ or } B) = 0.8$. Add probabilities: $0.2 + 0.6 = 0.8$.
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If $P(A \text{ or } B) = 1$, and $A$ and $B$ are mutually exclusive, what must be true?
If $P(A \text{ or } B) = 1$, and $A$ and $B$ are mutually exclusive, what must be true?
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$P(A) + P(B) = 1$. They form complementary exhaustive events.
$P(A) + P(B) = 1$. They form complementary exhaustive events.
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State the probability of intersection for mutually exclusive events.
State the probability of intersection for mutually exclusive events.
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$P(A \text{ and } B) = 0$. No common outcomes exist between the events.
$P(A \text{ and } B) = 0$. No common outcomes exist between the events.
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Identify if the events are mutually exclusive: flipping heads and tails on one coin toss.
Identify if the events are mutually exclusive: flipping heads and tails on one coin toss.
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Yes, they are mutually exclusive. One coin flip produces exactly one outcome.
Yes, they are mutually exclusive. One coin flip produces exactly one outcome.
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If $A$ and $B$ are mutually exclusive, does $P(A \text{ and } B) > 0$? Yes or No.
If $A$ and $B$ are mutually exclusive, does $P(A \text{ and } B) > 0$? Yes or No.
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No. Intersection probability is always zero.
No. Intersection probability is always zero.
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If events are mutually exclusive, what is their joint probability?
If events are mutually exclusive, what is their joint probability?
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Zero. Events have no intersection by definition.
Zero. Events have no intersection by definition.
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Find $P(A \text{ or } B)$ if $P(A)=0.3$, $P(B)=0.2$, and $A$ and $B$ are mutually exclusive.
Find $P(A \text{ or } B)$ if $P(A)=0.3$, $P(B)=0.2$, and $A$ and $B$ are mutually exclusive.
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$P(A \text{ or } B) = 0.5$. Add probabilities: $0.3 + 0.2 = 0.5$.
$P(A \text{ or } B) = 0.5$. Add probabilities: $0.3 + 0.2 = 0.5$.
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Are rolling an even number and an odd number on a die mutually exclusive?
Are rolling an even number and an odd number on a die mutually exclusive?
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Yes, they are mutually exclusive. No number can be both even and odd.
Yes, they are mutually exclusive. No number can be both even and odd.
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For mutually exclusive events, what does $P(A \text{ or } B)$ equal?
For mutually exclusive events, what does $P(A \text{ or } B)$ equal?
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$P(A) + P(B)$. No intersection allows direct addition of probabilities.
$P(A) + P(B)$. No intersection allows direct addition of probabilities.
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Identify if selecting a red or blue ball from a bag is mutually exclusive.
Identify if selecting a red or blue ball from a bag is mutually exclusive.
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Yes, it is mutually exclusive. One ball cannot have multiple colors.
Yes, it is mutually exclusive. One ball cannot have multiple colors.
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If events $A$ and $B$ are mutually exclusive, what is $P(A \text{ or } B)$?
If events $A$ and $B$ are mutually exclusive, what is $P(A \text{ or } B)$?
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$P(A) + P(B)$. No intersection term needed for mutually exclusive events.
$P(A) + P(B)$. No intersection term needed for mutually exclusive events.
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Are selecting a king or an ace from a deck mutually exclusive?
Are selecting a king or an ace from a deck mutually exclusive?
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Yes, they are mutually exclusive. One card cannot have multiple ranks.
Yes, they are mutually exclusive. One card cannot have multiple ranks.
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What must be true about $P(A \text{ and } B)$ for mutually exclusive events?
What must be true about $P(A \text{ and } B)$ for mutually exclusive events?
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It must be zero. Defining requirement for mutual exclusivity.
It must be zero. Defining requirement for mutual exclusivity.
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If $A$ and $B$ are mutually exclusive with $P(A)=0.6$, find $P(B)$ if $P(A \text{ or } B)=0.9$.
If $A$ and $B$ are mutually exclusive with $P(A)=0.6$, find $P(B)$ if $P(A \text{ or } B)=0.9$.
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$P(B) = 0.3$. Solve $0.9 = 0.6 + P(B)$ to get $P(B) = 0.3$.
$P(B) = 0.3$. Solve $0.9 = 0.6 + P(B)$ to get $P(B) = 0.3$.
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Are drawing a face card or a non-face card mutually exclusive?
Are drawing a face card or a non-face card mutually exclusive?
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Yes, they are mutually exclusive. Face and non-face cards are complementary categories.
Yes, they are mutually exclusive. Face and non-face cards are complementary categories.
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Can mutually exclusive events have non-zero intersection probability?
Can mutually exclusive events have non-zero intersection probability?
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No, the intersection probability is zero. By definition, intersection probability must be zero.
No, the intersection probability is zero. By definition, intersection probability must be zero.
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If $P(A)=0.4$ and $P(B)=0.5$ and they are mutually exclusive, find $P(A \text{ or } B)$.
If $P(A)=0.4$ and $P(B)=0.5$ and they are mutually exclusive, find $P(A \text{ or } B)$.
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$P(A \text{ or } B) = 0.9$. Add probabilities: $0.4 + 0.5 = 0.9$.
$P(A \text{ or } B) = 0.9$. Add probabilities: $0.4 + 0.5 = 0.9$.
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What is the joint probability of mutually exclusive events?
What is the joint probability of mutually exclusive events?
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Zero. Events cannot occur simultaneously.
Zero. Events cannot occur simultaneously.
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