Lesson
Notes
“At least one”
\(\hspace{10pt}1-p(0)\)
Sample Problems
\(\small{\textbf{1)}}\) If you flip a coin 5 times, find the probability of getting at least one tail. \(1-P(0)=1-.5^5=1-.03125=\textbf{.96875}\)
\(\small{\textbf{2)}}\) If you roll a die 8 times, find the probability of getting at least one 6. \(1-P(0)=1-\left(\frac{5}{6}\right)^8\approx 1-.2326\approx\textbf{.7674}\)
\(\small{\textbf{3)}}\) You have a deck of cards. You choose 20 cards. What is the probability of getting at least 1 ace card? \(1-P(0)=1-\left(\displaystyle\frac{{}_{4}C_{0} \cdot {}_{48}C_{4}}{{}_{52}C_{4}}\right)\approx 1-.7187\approx\textbf{.2813}\)
\(\small{\textbf{4)}}\) A multiple-choice quiz has 5 questions with 4 answer choices each. What is the probability of guessing and getting at least one correct? \(1-P(0)=1-\left(\frac{3}{4}\right)^5=1-.2373=\textbf{.7627}\)
\(\small{\textbf{5)}}\) A light bulb has a 2% chance of failing on any given day. What is the probability it fails at least once in 50 days? \(1-P(0)=1-(.98)^{50}\approx 1-.3642=\textbf{.6358}\)
\(\small{\textbf{6)}}\) You randomly select 3 digits from 0–9 (with replacement). What is the probability of getting at least one 7? \(1-P(0)=1-\left(\frac{9}{10}\right)^3=1-.729=\textbf{.271}\)
\(\small{\textbf{7)}}\) A basketball player has a 70% free-throw success rate. If they shoot 4 times, what’s the probability of making at least one shot? \(1-P(0)=1-(.3)^4=1-.0081=\textbf{.9919}\)
\(\small{\textbf{8)}}\) A security system detects intrusions with 95% accuracy. If there are 3 intrusion attempts, what’s the probability that at least one is detected? \(1-P(0)=1-(.05)^3=1-.000125=\textbf{.999875}\)
See Related Pages\(\)
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