Topics
8. Discrete random variables
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AustraliaVIC
VCE 12 Methods 2023

8.07 Applications of binomial distributions

Lesson
Worksheet
Practice

Interactive practice questions

A standard six-sided die is rolled $5$5 times.

a

What is the probability of rolling exactly $3$3 ones?

Round your answer to four decimal places.

b

What is the probability of rolling less than $3$3 ones?

Round your answer to four decimal places.

c

What is the probability of rolling no more than $3$3 ones?

Round your answer to four decimal places.

Easy
7min

Adam has product tested the name of his new product and has found that $61%$61% of people like it. Assuming his product test results are correct, if he randomly asks $50$50 people if they like the name of his new product, what is the probability that exactly $24$24 people will say they like the name?

Give your answer to four decimal places.

Easy
1min

$72%$72% of the fans attending a particular concert are male. If a security guard decides to randomly check exactly $10$10 fans’ bags for prohibited items, what is the probability that he checks exactly $5$5 females' bags?

Give your answer to four decimal places.

Easy
1min

The founders of a dating app claim that $39%$39% of messages are replied to. Assuming that this is correct, if Aaron sends $30$30 messages to different people, what is the probability that he will get replies to exactly half of his messages?

Give your answer to four decimal places.

Easy
1min
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Outcomes

U34.AoS4.5

the concepts of a random variable (discrete and continuous), Bernoulli trials and probability distributions, the parameters used to define a distribution and properties of probability distributions and their graphs

U34.AoS4.2

discrete random variables: - specification of probability distributions for discrete random variables using graphs, tables and probability mass functions - calculation and interpretation of mean, 𝜇, variance, 𝜎^2, and standard deviation of a discrete random variable and their use - Bernoulli trials and the binomial distribution, Bi(𝑛, 𝑝), as an example of a probability distribution for a discrete random variable - effect of variation in the value(s) of defining parameters on the graph of a given probability mass function for a discrete random variable - calculation of probabilities for specific values of a random variable and intervals defined in terms of a random variable, including conditional probability

U34.AoS4.6

the conditions under which a Bernoulli trial or a probability distribution may be selected to suitably model various situations

U34.AoS4.11

apply probability distributions to modelling and solving related problems

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