Answer :
The probability that the student will answer at least7questions correctly then the probability is = [tex]\frac{120}{128}[/tex]
A probability is a number that reflects the chance or likelihood that a particular event will occur. Probabilities can be expressed as proportions that range from 0 to 1, and they can also be expressed as percentages ranging from 0% to 100%.
Given that,
A test consists of 10 true/false questions.
If a student guesses on each question
The probability that the student will answer at least7questions correctly.
The probability that the student answers each question correctly is 1/2, and
The probability that the student answers each question correctly is also 1/2
{Bernoalli trail}
Bernoalli trail for at least 7 times,
Probability P = [tex]C7_{10} (\frac{1}{2}) ^{7} (\frac{1}{2}) ^{7}[/tex]
Using the formula nCr = n!(n−r)!r!
= 10!(10−7)!7!
Subtract 7 from 10.
= 10!(3)!7!
Simplify 10!(3)!7!.
Rewrite 10! as (10⋅9⋅8⋅7!)
= (10⋅9⋅8⋅7! / (3)!7!)
Cancel the common factor of 7!.
Cancel the common factor.
= 10⋅9⋅8⋅7! / (3)!7!
Rewrite the expression.
= 10⋅9⋅8 / (3)!
Multiply 10 by 9.
= 90⋅8 / (3)!
Multiply 90 by 8.
= 720 / (3)!
Expand (3)! to 3⋅2⋅1.
= 720 / 3⋅2⋅1
Multiply 3 by 2.
= 720 / 6⋅1
= 720 / 6
Divide 720 by 6
= 120
So,
We can write,
P = [tex]\frac{120}{2^{7} }[/tex]
P = [tex]\frac{120}{128}[/tex]
Therefore,
The probability that the student will answer at least7questions correctly then the probability is = [tex]\frac{120}{128}[/tex]
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