This quiz has 9 questions with 4 options for each question. if a student chooses answers randomly, what is the probability that he will get at least 7 answers correct

This question is solved using a binomial distribution, and you must use a calculator.

[tex]X \sim Bi (9, \frac{1}{4} )[/tex]

The required probability which you can find using your calculator is

[tex]Pr(X \geq 7)[/tex]

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MrRoyal MrRoyal · Answer 2 · 2022-01-07T15:36:08+01:00

The probability that a student gets at least 7 answers correctly is 0.1343%

The number of questions is given as:

[tex]n = 9[/tex]

Since there are four options, the probability that a student chooses the right option is:

[tex]p = \frac 14[/tex]

[tex]p = 0.25[/tex]

The probability that a student gets at least 7 answers correctly is represented as: P(x >= 7)

This is calculated using the following binomial probability:

[tex]P(x = r) = ^nC_r p^x \times (1 - p)^{n - r}[/tex]

So, we have:

[tex]P(x \ge 7) = ^9C_7 (0.25)^7 \times (1 - 0.25)^2 + ^9C_8 (0.25)^8 \times (1 - 0.25) + ^9C_9 (0.25)^9 \times (1 - 0.25)^0[/tex]

This gives

[tex]P(x \ge 7) = 0.00134277343[/tex]

Express as percentage

[tex]P(x \ge 7) = 0.134277343\%[/tex]

Approximate

[tex]P(x \ge 7) = 0.1343\%[/tex]

Hence, the probability that a student gets at least 7 answers correctly is 0.1343%