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8.03 Applications of binomial distributions

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 rollingΒ 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

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

$64%$64% of penguins in a particular enclosure are female.

If $6$6 of the penguins are chosen at random for health checks, what is the probability that exactly $3$3 of them will be female? Give your answer to four decimal places.

Easy
1min
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Outcomes

4.3.2.3

determine and use the probabilities 𝑃(𝑋=π‘Ÿ) = {nr} 𝑝^π‘Ÿ(1 βˆ’ 𝑝)^(n-r) associated with the binomial distribution with parameters 𝑛 and p

4.3.2.4

calculate the mean 𝑛p and variance 𝑛p(1βˆ’π‘) of a binomial distribution using technology and algebraic methods

4.3.2.5

identify contexts suitable to model binomial distributions and associated probabilities to solve practical problems, including the language of β€˜at most’ and β€˜at least’

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