Question

30) A student has not been to class and must pass a 20 question true/false exam to continue in the course. The student will guess on every question and must get at least 14 correct to pass the test. What is the probability that the student will pass the test

Answer 1

The probability that the student will pass the test is 0.057

In probability theory and statistics, the Bernoulli distribution, named after Swiss mathematician Jacob Bernoulli,[1] is the discrete probability distribution of a random variable which takes the value 1 with probability $p$ and the value 0 with probability ${\displaystyle q=1-p}$. Less formally, it can be thought of as a model for the set of possible outcomes of any single experiment that asks a yes–no question. Such questions lead to outcomes that are boolean-valued: a single bit whose value is success/yes/true/one with probability p and failure/no/false/zero with probability q.

The student will pass if he at least answers 14 questions correctly .

This can be written as a Bernoulli distribution function $P(Q=i)= 20C_{i} (\frac{1}{2} )^i(1-\frac{1}{2} )^(20-i)$

P(Q≥ 14) = P(Q=14) + P(Q=15) + P(Q=16) +P(Q=17) + P(Q=18)+ P(Q=19) +   P(Q=20)

 P(Q=14) = 20$C_{14}$$(1/2)^{20}$

 P(Q=15) = 20$C_{15}$$(1/2)^{20}$

 P(Q=16) = 20$C_{16}$$(1/2)^{20}$

 P(Q=17) = 20$C_{17}$$(1/2)^{20}$

 P(Q=18) = 20$C_{18}$$(1/2)^{20}$

 P(Q=19) = 20$C_{19}$$(1/2)^{20}$

 P(Q=20) = $20C_{20}(1/2)^{20}$

On summing up all we get,

P(Q≥ 14) = (38760 + 15504 + 4845+ 1140 + 190 + 20 + 1)/2^(20)

= 15115/262144=0.057

Thus the probability that the student will pass the test is 0.057

Learn more about Bernoulli distribution  here :

https://brainly.com/question/24232842

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