Question

A student takes a ten-question true-false quiz, but did not study and randomly guesses each answer. Find the probability that the student passes the quiz with a grade of at least 40% of the questions correct. (Round your answer to three decimal places.)

Answer #1

Solution:

Each question has two choices . TRUE and FALSE

So , probability of getting correct answer is p = 1/2 = 0.5

There are 10 questions.

n = 10

Let X be the number of correct answers .

So , X follows Binomial(10 , 0.5)

Using binomial probability formula ,

P(X = x) = (_{n} C _{x}) * p^{x} * (1 -
p)^{n - x} ; x = 0 ,1 , 2 , ....., n

Now ,

P(At least 40% of the questions correct)

= P(At least 40% of 10 )

= P(At least 4 questions correct)

= P(X 4)

= 1 - { P(X < 4) }

= 1 - { P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) }

= 1 - { (_{10} C _{0}) * 0.5^{0} * (1 -
0.5)^{10 - 0} + (_{10} C _{1}) *
0.5^{1} * (1 - 0.5)^{10 - 1} + (_{10} C
_{2}) * 0.5^{2} * (1 - 0.5)^{10 - 2} +
(_{10} C _{3}) * 0.5^{3} * (1 - 0.5)^{10
- 3} }

= 1 - {0.0009765625 + 0.009765625 + 0.0439453125 + 0.1171875 }

= 1 - {0.171875 }

= **0.828**

A student takes a 40-question multiple-choice exam but did not
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possible choices for the answer. Find the probability that the
student guesses more than 75% of the questions correctly. (Round
your answer to three decimal places.)

a) At The Fencing Center, 60% of the fencers use the foil as
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Find the probability that nine do not use the
foil as their main weapon. (Round your answer to four decimal
places.)
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a.
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b.
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d.
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