Flashcards · Maths · Probability
Conditional Probability
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What is a conditional probability?
The probability of an event given that something else has happened or is known.
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What does \(P(A \mid B)\) mean?
The probability of \(A\) given \(B\).
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What does "given that" do to the group you look at?
It makes it smaller, to just those that satisfy the condition.
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What is the bottom of a conditional probability fraction?
The number in the given group.
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Out of 14 tennis players, 6 also play football. What is \(P(F \mid T)\)?
\(\dfrac{6}{14} = \dfrac{3}{7}\).
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Is \(P(A \mid B)\) always equal to \(P(B \mid A)\)?
No, they use different groups.
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What is the formula for \(P(A \text{ and } B)\) using conditional probability (Higher tier)?
\(P(A \mid B) \times P(B)\).
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How do you rearrange it to find \(P(A \mid B)\) (Higher tier)?
\(\dfrac{P(A \text{ and } B)}{P(B)}\).
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What is the condition for two events to be independent?
\(P(A \mid B) = P(A)\), or \(P(A \text{ and } B) = P(A) \times P(B)\).
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What are the second-stage probabilities on a tree without replacement?
Conditional probabilities.
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Of 50 people who drive, 20 are female. What is the probability that a driver is male?
\(\dfrac{30}{50} = \dfrac{3}{5}\).
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A person who drives is chosen. Why is the denominator 50 and not 100?
Only the drivers are in the group.
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In a tree with 3 red and 2 blue, what is \(P(\text{second red} \mid \text{first red})\)?
\(\dfrac{2}{4} = \dfrac{1}{2}\).
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If \(P(A) = 0.5\), \(P(B) = 0.4\) and \(P(A \text{ and } B) = 0.2\), are they independent?
Yes, because \(0.5 \times 0.4 = 0.2\).
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How do you find the total of the group when you are told the second pick was red?
Add all the paths that end in red.
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Which tools can you use to find conditional probabilities?
Venn diagrams, two-way tables and tree diagrams.