A test consists of 10 true/false questions. To pass the test a student must answer at least 6 questions correctly. If a student guesses on each question, what is the probability that the student will pass the test?

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Answer 1

Answer:

Answer:

37.70% probability that the student will pass the test

Step-by-step explanation:

For each question, there are only two possible outcomes. Either the student guesses it correctly, or he does not. The probability of a student guessing a question correctly is independent of other questions. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_(n,x).p^(x).(1-p)^(n-x)$

In which $C_(n,x)$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_(n,x) = (n!)/(x!(n-x)!)$

And p is the probability of X happening.

10 true/false questions.

10 questions, so $n = 10$

True/false questions, 2 options, one of which is correct. So $p = (1)/(2) = 0.5$

If a student guesses on each question, what is the probability that the student will pass the test?

$P(X \geq 6) = P(X = 6) + P(X = 7) + P(X = 8) + P(X = 9) + P(X = 10)$

$P(X = x) = C_(n,x).p^(x).(1-p)^(n-x)$

$P(X = 6) = C_(10,6).(0.5)^(6).(0.5)^(4) = 0.2051$

$P(X = 7) = C_(10,7).(0.5)^(7).(0.5)^(3) = 0.1172$

$P(X = 8) = C_(10,8).(0.5)^(8).(0.5)^(2) = 0.0439$

$P(X = 9) = C_(10,9).(0.5)^(9).(0.5)^(1) = 0.0098$

$P(X = 10) = C_(10,10).(0.5)^(10).(0.5)^(0) = 0.0010$

$P(X \geq 6) = P(X = 6) + P(X = 7) + P(X = 8) + P(X = 9) + P(X = 10) = 0.2051 + 0.1172 + 0.0439 + 0.0098 + 0.0010 = 0.3770$

37.70% probability that the student will pass the test

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Step-by-step explanation:

9 (x + 1) = 9*x + 9*1 = 9x + 9

Which polygons have at least one pair of parallel sides but are not parallelograms? Choose all that apply.

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The correct option is polygon E.

What are polygons?

A polygon is a plane figure that is described by a finite number of straight line segments connected to form a closed polygonal chain.

Given that, Which polygons have at least one pair of parallel sides but are not parallelograms,

Such polygons are called trapezoid.

A trapezoid, also known as a trapezium, is a flat-closed shape having 4 straight sides, with one pair of parallel sides.

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