NZ Level 8 (NZC) Level 3 (NCEA) [In development] 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.

a

What is the probability that he achieves full marks?

b

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

c

What is the probability that he passes the quiz?

Easy
Approx 7 minutes

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?

### Outcomes

#### S8-4

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

#### 91586

Apply probability distributions in solving problems