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The random variable X represents the number of successes in 10 independent Bernoulli trials - HSC - SSCE Mathematics Extension 1 - Question 8 - 2021 - Paper 1

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The random variable X represents the number of successes in 10 independent Bernoulli trials. The probability of success is $p = 0.9$ in each trial. Let $r = P(X ex... show full transcript

Worked Solution & Example Answer:The random variable X represents the number of successes in 10 independent Bernoulli trials - HSC - SSCE Mathematics Extension 1 - Question 8 - 2021 - Paper 1

Step 1

Which of the following describes the value of r?

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Answer

To determine the value of r=P(X≥1)r = P(X ≥ 1), we can first calculate its complement:

P(X<1)=P(X=0)=(1−p)n=(1−0.9)10=0.110=0.0000000001P(X < 1) = P(X = 0) = (1 - p)^{n} = (1 - 0.9)^{10} = 0.1^{10} = 0.0000000001

Thus, we have:

P(X≥1)=1−P(X=0)=1−0.0000000001≈1P(X ≥ 1) = 1 - P(X = 0) = 1 - 0.0000000001 ≈ 1

Since rr is almost equal to 1, it follows that r>0.9r > 0.9 and specifically is definitely in the range 0.1<r<0.90.1 < r < 0.9. Therefore, the correct choice is C.

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