Quick questions on Bernoulli trials and the binomial distribution: VCE Math Methods Unit 3

5short Q&A pairs drawn directly from our worked dot-point answer. For full context and worked exam questions, read the parent dot-point page.

What is wrong formula direction?

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E(X) = n p

, not

E(X) = p

E(X) = n

. Likewise variance has both

n

and

p(1 - p)

What are boundary errors on cumulative probabilities?

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"At least 3" means

X \geq 3

, which is

1 - P(X \leq 2)

. Subtracting

P(X \leq 3)

instead loses the

P(X = 3)

term.

What is q1?

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For

X \sim \mathrm{Bi}(8, 0.5)

, find

P(X = 4)

. [2 marks]

What is q2?

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A goalkeeper saves

20\%

of shots. In

10

shots, find

E(X)

and

\mathrm{Var}(X)

for the number saved. [2 marks]

What is q3?

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A quiz has

12

true/false questions answered by guessing. Find the probability of at least

10

correct. [3 marks]

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