Conditional Probability, Independence, and Bayes' Formula

Questions

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• Question 1 of 11 · Intro

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  Garden Tool Loan

  Of 30 volunteers assigned to the community garden, 13 borrowed a tool kit. Given that a randomly selected volunteer is assigned to the garden, what is the probability that the volunteer borrowed a tool kit?

• Question 2 of 11 · Intro

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  Greenhouse Germination Probability

  A greenhouse places 40% of seeds in tray A and the rest in tray B. A seed germinates with probability 0.7 in tray A and 0.1 in tray B. What is the probability that a randomly selected seed germinates?

• Question 3 of 11 · Intro

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  Independent Badge and Coffee Choices

  At an event, a visitor independently receives a blue badge with probability 0.4 and chooses coffee with probability 0.3. What is the probability that the visitor receives a blue badge and chooses coffee?

• Question 4 of 11 · Intro

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  Library Return Probability

  A library sends 25% of reminders by text and the rest by email. A borrowed item is returned that day with probability 0.9 after a text reminder and 0.3 after an email reminder. What is the probability that a randomly selected reminded item is returned that day?

• Question 5 of 11 · Intro

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  Maintenance Flag Update

  Ten percent of machines need maintenance. A monitor flags a machine with probability 0.9 when maintenance is needed and with probability 0.05 otherwise. Given that a machine is flagged, what is the probability that it needs maintenance?

• Question 6 of 11 · Intro

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  Portfolio Shortlist Update

  Twenty-five percent of submitted portfolios use format A. A portfolio is shortlisted with probability 0.75 when it uses format A and with probability 0.15 otherwise. Given that a portfolio was shortlisted, what is the probability that it used format A?

• Question 7 of 11 · Intro

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  Repair Routing Probability

  A service desk routes 30% of requests to team A and the rest to team B. Team A resolves a request on the first attempt with probability 0.8, while team B does so with probability 0.2. What is the probability that a randomly selected request is resolved on the first attempt?

• Question 8 of 11 · Intro

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  Second Express Ticket

  A box holds 9 standard tickets and 3 express tickets. Two tickets are drawn without replacement. Given that the first ticket is standard, what is the probability that the second ticket is express?

• Question 9 of 11 · Intro

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  Workshop Completion Probability

  A workshop assigns 60% of participants to a guided track and the rest to a self-paced track. Completion probabilities are 0.5 for the guided track and 0.15 for the self-paced track. What is the probability that a randomly selected participant completes the workshop?

• Question 10 of 11 · Core

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  Campus badge flag

  A campus event scanner flags 6% of regular badges and 92% of priority badges. If 8% of badges are priority badges, what is the probability that a flagged badge is priority?

• Question 11 of 11 · Core

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  Message routing label

  A message router labels 90% of priority messages and 7% of regular messages for quick handling. If 15% of messages are priority messages, what is the probability that a labeled message is priority?