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A student randomly guesses on 10 true or false questions use the bionomial model to find the probability that the student gets 7 out of the 10 questions right

A student randomly guesses on 10 true or false questions use the bionomial model to-example-1
User Apoorva
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1 Answer

1 vote

Option A: 11.8%

Explanation:

The total number of question n=10

The probability of getting true is
p=(1)/(2)

The probability of getting false is
q=(1)/(2)

It is given that the student gets 7 out of 10 questions right, the,
x=7

Using binomial distribution formula,


P(x)=\left[(n !)/(x !(n-x) !)\right] p^(x) q^(n-x)

Substituting the values, we get,


\begin{aligned}P(7) &=\left[(10 !)/(7 !(10-7) !)\right]\left((1)/(2)\right)^(7)\left((1)/(2)\right)^(3) \\&=\left[(10 !)/(7 ! 3 !)\right]\left((1)/(2)\right)^(7+3)\end{aligned}

Solving, we get,


P(7)=(15)/(128)


P(7)=0.118

To find the probability, multiply it by 100, we get,


0.118*100=11.8%

Thus, the correct answer is 11.8%

User Dejo
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