how do i find the probability for questions like this? A test consist of 10 true/false questions. to pass the test a student must answer at least 9...

Sunday, June 7, 2015

how do i find the probability for questions like this? A test consist of 10 true/false questions. to pass the test a student must answer at least 9...

We need to
find the probability that the student guesses correctly on 9 or 10 true false
questions:

(1) The most straightforward way is to use the binomial
distribution. Given the probability p of some event e, the probability of getting x events in n
trials is given as:

$\displaystyle{P}{\left({e}={x}\right)}=$ $\displaystyle_{n}{C}_{{x}}{\left({{p}}^{{x}}\right)}{{\left({1}-{p}\right)}}^{{{n}-{x}}}$

Here x=9 or 10, n=10, and the probability is p=.5 as there is an equally likely chance
of getting the question right or wrong. Since we have 9 or 10, and the events are mutually
exclusive, the total probability is P(x=9)+P(x=10).

$\displaystyle{P}{\left({x}={9}\right)}=$ $\displaystyle_{\left({10}\right)}{C}_{{9}}{{.5}}^{{9}}$
.5^1=(10)(1/512)(1/2)=5/512~~.00977