Applying the Addition Rule for Probability - Statistics
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Find $P(A\text{ or }B)$ if $P(A)=0.40$, $P(B)=0.35$, and $P(A\text{ and }B)=0.10$.
Find $P(A\text{ or }B)$ if $P(A)=0.40$, $P(B)=0.35$, and $P(A\text{ and }B)=0.10$.
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$0.65$. $0.40+0.35-0.10=0.65$ by Addition Rule.
$0.65$. $0.40+0.35-0.10=0.65$ by Addition Rule.
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Find $P(A\text{ or }B)$ if $P(A)=0.90$, $P(B)=0.30$, and $P(A\text{ and }B)=0.25$.
Find $P(A\text{ or }B)$ if $P(A)=0.90$, $P(B)=0.30$, and $P(A\text{ and }B)=0.25$.
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$0.95$. $0.90+0.30-0.25=0.95$ by Addition Rule.
$0.95$. $0.90+0.30-0.25=0.95$ by Addition Rule.
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Identify the condition that makes $P(A \text{ and } B)=0$ in the Addition Rule.
Identify the condition that makes $P(A \text{ and } B)=0$ in the Addition Rule.
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$A$ and $B$ are mutually exclusive (disjoint). Events can't happen simultaneously.
$A$ and $B$ are mutually exclusive (disjoint). Events can't happen simultaneously.
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State the Addition Rule formula for $P(A \text{ or } B)$ in terms of $P(A)$, $P(B)$, and $P(A \text{ and } B)$.
State the Addition Rule formula for $P(A \text{ or } B)$ in terms of $P(A)$, $P(B)$, and $P(A \text{ and } B)$.
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$P(A\text{ or }B)=P(A)+P(B)-P(A\text{ and }B)$. Subtract overlap to avoid counting twice.
$P(A\text{ or }B)=P(A)+P(B)-P(A\text{ and }B)$. Subtract overlap to avoid counting twice.
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What is the formula for $P(A \text{ and } B)$ rewritten from the Addition Rule?
What is the formula for $P(A \text{ and } B)$ rewritten from the Addition Rule?
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$P(A\text{ and }B)=P(A)+P(B)-P(A\text{ or }B)$. Rearrange the Addition Rule by solving for $P(A\text{ and }B)$.
$P(A\text{ and }B)=P(A)+P(B)-P(A\text{ or }B)$. Rearrange the Addition Rule by solving for $P(A\text{ and }B)$.
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What is the formula for $P(A \text{ or } B)$ when $A$ and $B$ are mutually exclusive?
What is the formula for $P(A \text{ or } B)$ when $A$ and $B$ are mutually exclusive?
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$P(A\text{ or }B)=P(A)+P(B)$. No overlap when events can't occur together.
$P(A\text{ or }B)=P(A)+P(B)$. No overlap when events can't occur together.
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Identify the error: A student used $P(A\text{ or }B)=P(A)+P(B)$ when $P(A\text{ and }B)\neq 0$.
Identify the error: A student used $P(A\text{ or }B)=P(A)+P(B)$ when $P(A\text{ and }B)\neq 0$.
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Missing subtraction of $P(A\text{ and }B)$. Must subtract overlap when events aren't disjoint.
Missing subtraction of $P(A\text{ and }B)$. Must subtract overlap when events aren't disjoint.
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Find $P(A\text{ or }B)$ if $P(A)=0.20$, $P(B)=0.50$, and $A$ and $B$ are mutually exclusive.
Find $P(A\text{ or }B)$ if $P(A)=0.20$, $P(B)=0.50$, and $A$ and $B$ are mutually exclusive.
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$0.70$. $0.20+0.50-0=0.70$ since mutually exclusive.
$0.70$. $0.20+0.50-0=0.70$ since mutually exclusive.
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Find $P(A\text{ or }B)$ if $P(A)=\frac{1}{4}$, $P(B)=\frac{1}{3}$, and $P(A\text{ and }B)=\frac{1}{12}$.
Find $P(A\text{ or }B)$ if $P(A)=\frac{1}{4}$, $P(B)=\frac{1}{3}$, and $P(A\text{ and }B)=\frac{1}{12}$.
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$\frac{1}{2}$. $\frac{1}{4}+\frac{1}{3}-\frac{1}{12}=\frac{3+4-1}{12}=\frac{1}{2}$.
$\frac{1}{2}$. $\frac{1}{4}+\frac{1}{3}-\frac{1}{12}=\frac{3+4-1}{12}=\frac{1}{2}$.
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Find $P(A\text{ and }B)$ if $P(A)=0.55$, $P(B)=0.30$, and $P(A\text{ or }B)=0.70$.
Find $P(A\text{ and }B)$ if $P(A)=0.55$, $P(B)=0.30$, and $P(A\text{ or }B)=0.70$.
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$0.15$. $0.55+0.30-0.70=0.15$ by rearranging.
$0.15$. $0.55+0.30-0.70=0.15$ by rearranging.
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Which probability is subtracted in $P(A\text{ or }B)=P(A)+P(B)-\square$ to avoid double counting?
Which probability is subtracted in $P(A\text{ or }B)=P(A)+P(B)-\square$ to avoid double counting?
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$P(A\text{ and }B)$. Overlap is counted in both $P(A)$ and $P(B)$.
$P(A\text{ and }B)$. Overlap is counted in both $P(A)$ and $P(B)$.
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What is the meaning of $P(A \text{ or } B)$ in words (inclusive or)?
What is the meaning of $P(A \text{ or } B)$ in words (inclusive or)?
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Probability that at least one of $A$ or $B$ occurs. Union includes either or both events.
Probability that at least one of $A$ or $B$ occurs. Union includes either or both events.
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What is the meaning of $P(A \text{ and } B)$ in words?
What is the meaning of $P(A \text{ and } B)$ in words?
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Probability that both $A$ and $B$ occur. The intersection of events $A$ and $B$.
Probability that both $A$ and $B$ occur. The intersection of events $A$ and $B$.
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Find $P(A\text{ and }B)$ if $P(A)=\frac{3}{5}$, $P(B)=\frac{1}{2}$, and $P(A\text{ or }B)=\frac{4}{5}$.
Find $P(A\text{ and }B)$ if $P(A)=\frac{3}{5}$, $P(B)=\frac{1}{2}$, and $P(A\text{ or }B)=\frac{4}{5}$.
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$\frac{3}{10}$. $\frac{3}{5}+\frac{1}{2}-\frac{4}{5}=\frac{6+5-8}{10}=\frac{3}{10}$.
$\frac{3}{10}$. $\frac{3}{5}+\frac{1}{2}-\frac{4}{5}=\frac{6+5-8}{10}=\frac{3}{10}$.
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Find $P(A\text{ or }B)$ if $P(A)=0.15$, $P(B)=0.10$, and $P(A\text{ and }B)=0$.
Find $P(A\text{ or }B)$ if $P(A)=0.15$, $P(B)=0.10$, and $P(A\text{ and }B)=0$.
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$0.25$. $0.15+0.10-0=0.25$ for disjoint events.
$0.25$. $0.15+0.10-0=0.25$ for disjoint events.
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Find $P(A\text{ or }B)$ from counts: $n(A)=25$, $n(B)=30$, $n(A\cap B)=10$, total $n=60$.
Find $P(A\text{ or }B)$ from counts: $n(A)=25$, $n(B)=30$, $n(A\cap B)=10$, total $n=60$.
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$\frac{3}{4}$. $\frac{25+30-10}{60}=\frac{45}{60}=\frac{3}{4}$.
$\frac{3}{4}$. $\frac{25+30-10}{60}=\frac{45}{60}=\frac{3}{4}$.
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Interpretation check: If $P(A\text{ or }B)=0.72$, what does $0.72$ represent in context?
Interpretation check: If $P(A\text{ or }B)=0.72$, what does $0.72$ represent in context?
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Chance that at least one of $A$ or $B$ occurs. Probability that event $A$ or event $B$ happens.
Chance that at least one of $A$ or $B$ occurs. Probability that event $A$ or event $B$ happens.
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Find $P(A\text{ and }B)$ if $P(A)=0.48$, $P(B)=0.52$, and $P(A\text{ or }B)=0.80$.
Find $P(A\text{ and }B)$ if $P(A)=0.48$, $P(B)=0.52$, and $P(A\text{ or }B)=0.80$.
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$0.20$. $0.48+0.52-0.80=0.20$ by rearranging.
$0.20$. $0.48+0.52-0.80=0.20$ by rearranging.
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Find $P(A\text{ or }B)$ if $A\subseteq B$, $P(A)=0.20$, and $P(B)=0.60$.
Find $P(A\text{ or }B)$ if $A\subseteq B$, $P(A)=0.20$, and $P(B)=0.60$.
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$0.60$. Since $A\subseteq B$, $A\cup B=B$.
$0.60$. Since $A\subseteq B$, $A\cup B=B$.
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Choose the correct statement: If $A\subseteq B$, what is $P(A\text{ or }B)$ equal to?
Choose the correct statement: If $A\subseteq B$, what is $P(A\text{ or }B)$ equal to?
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$P(B)$. If $A$ is subset of $B$, union equals $B$.
$P(B)$. If $A$ is subset of $B$, union equals $B$.
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Find $P(A\text{ or }B)$ given $P(A)=0.40$, $P(B)=0.30$, and $P(A\text{ and }B)=0.10$.
Find $P(A\text{ or }B)$ given $P(A)=0.40$, $P(B)=0.30$, and $P(A\text{ and }B)=0.10$.
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$0.60$. Apply: $0.40+0.30-0.10=0.60$.
$0.60$. Apply: $0.40+0.30-0.10=0.60$.
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Find $P(A\text{ or }B)$ if $A$ and $B$ are mutually exclusive with $P(A)=0.18$ and $P(B)=0.22$.
Find $P(A\text{ or }B)$ if $A$ and $B$ are mutually exclusive with $P(A)=0.18$ and $P(B)=0.22$.
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$0.40$. Mutually exclusive: just add $0.18+0.22=0.40$.
$0.40$. Mutually exclusive: just add $0.18+0.22=0.40$.
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Find $P(A\text{ or }B)$ given $P(A)=0.25$, $P(B)=0.50$, and $P(A\text{ and }B)=0.05$.
Find $P(A\text{ or }B)$ given $P(A)=0.25$, $P(B)=0.50$, and $P(A\text{ and }B)=0.05$.
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$0.70$. Apply: $0.25+0.50-0.05=0.70$.
$0.70$. Apply: $0.25+0.50-0.05=0.70$.
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State the Addition Rule formula for $P(A\text{ or }B)$ in terms of $P(A)$, $P(B)$, and $P(A\text{ and }B)$.
State the Addition Rule formula for $P(A\text{ or }B)$ in terms of $P(A)$, $P(B)$, and $P(A\text{ and }B)$.
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$P(A\text{ or }B)=P(A)+P(B)-P(A\text{ and }B)$. Subtracts overlap to avoid counting shared outcomes twice.
$P(A\text{ or }B)=P(A)+P(B)-P(A\text{ and }B)$. Subtracts overlap to avoid counting shared outcomes twice.
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What is the equivalent notation statement for $P(A\text{ or }B)$ using the union symbol?
What is the equivalent notation statement for $P(A\text{ or }B)$ using the union symbol?
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$P(A\cup B)$. Union symbol represents the set of outcomes in either event.
$P(A\cup B)$. Union symbol represents the set of outcomes in either event.
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What is $P(A\text{ or }B)$ if events $A$ and $B$ are mutually exclusive?
What is $P(A\text{ or }B)$ if events $A$ and $B$ are mutually exclusive?
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$P(A\text{ or }B)=P(A)+P(B)$. Mutually exclusive means no overlap, so $P(A\text{ and }B)=0$.
$P(A\text{ or }B)=P(A)+P(B)$. Mutually exclusive means no overlap, so $P(A\text{ and }B)=0$.
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What value does the Addition Rule subtract to correct for double counting in $P(A\text{ or }B)$?
What value does the Addition Rule subtract to correct for double counting in $P(A\text{ or }B)$?
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$P(A\text{ and }B)$. Removes the overlap where both events occur together.
$P(A\text{ and }B)$. Removes the overlap where both events occur together.
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Find $P(A\cup B)$ from a table where $P(A)=0.52$, $P(B)=0.27$, and $P(A\cap B)=0.12$.
Find $P(A\cup B)$ from a table where $P(A)=0.52$, $P(B)=0.27$, and $P(A\cap B)=0.12$.
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$0.67$. Apply: $0.52+0.27-0.12=0.67$.
$0.67$. Apply: $0.52+0.27-0.12=0.67$.
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Identify the correct expression for $P(A\text{ or }B)$ when $A$ and $B$ are independent.
Identify the correct expression for $P(A\text{ or }B)$ when $A$ and $B$ are independent.
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$P(A\text{ or }B)=P(A)+P(B)-P(A)P(B)$. For independent events, $P(A\text{ and }B)=P(A)P(B)$.
$P(A\text{ or }B)=P(A)+P(B)-P(A)P(B)$. For independent events, $P(A\text{ and }B)=P(A)P(B)$.
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Which inequality must always be true for valid events: $P(A\text{ or }B)\leq \ ?$
Which inequality must always be true for valid events: $P(A\text{ or }B)\leq \ ?$
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$P(A\text{ or }B)\leq 1$. Probability cannot exceed 1 (certainty).
$P(A\text{ or }B)\leq 1$. Probability cannot exceed 1 (certainty).
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