HPCET Complement Rule — practice questions

Explore 2 free Complement Rule questions in HPCET Mathematics. Open each question or exercise to read its content, reference answers and available explanation.

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Complement Rule questions and exercises with answers

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Two cards are drawn with replacement. $X$ = number of aces. The probability $P[X \geq 1]$ equals:Read the answer and worked solution →$P(X \geq 1) = 1 - P(X = 0)$ is an example of the:Read the answer and worked solution →

Worked practice questions

Two cards are drawn with replacement. $X$ = number of aces. The probability $P[X \geq 1]$ equals:

$25/169$
$1/169$
$144/169$
$24/169$

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Correct answer: A. $25/169$

$P[X \geq 1] = 1 - P[X=0] = 1 - 144/169 = 25/169$. (Or compute directly: $P[X=1] + P[X=2] = 24/169 + 1/169 = 25/169$.)

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$P(X \geq 1) = 1 - P(X = 0)$ is an example of the:

Multiplication rule
Complement rule (useful for 'at least one' problems)
Bayes' theorem
Inclusion-exclusion principle

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Correct answer: B. Complement rule (useful for 'at least one' problems)

The complement of 'at least one success' is 'no successes' — usually easier to compute as $q^n$. Then subtract from 1.