NZ Level 8 (NZC) Level 3 (NCEA) [In development]
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Applications of Bernoulli random variables and probabilities

Interactive practice questions

Paul is completing a quiz that consists of $7$7 multiple-choice questions and that has a pass mark of $4$4. Each question has $5$5 possible answers, only one of which is correct. As he was too lazy to study for the quiz, Paul randomly guesses the answer to every question.


What is the probability that he achieves full marks?


What is the probability that he gets all of them wrong?


What is the probability that he passes the quiz?

Approx 7 minutes
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A fair die is rolled $5$5 times.

A fair die is rolled $6$6 times.

Records show that half of all households in a city have broadband. What is the probability that less than $45%$45% of a sample of $100$100 random households have a broadband?

Give your answer as a decimal correct to four decimal places.



Investigate situations that involve elements of chance: A calculating probabilities of independent, combined, and conditional events B calculating and interpreting expected values and standard deviations of discrete random variables C applying distributions such as the Poisson, binomial, and normal


Apply probability distributions in solving problems

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