Answer to Question #314839 in Statistics and Probability for amiela

Question

a survey unofficially claimed that in every five (5) young executives , only one (1) practices good reading habits.

what is the probability that out of 10 10 young executives , two executives practice good reading habits

Answer 1

The pribability that aexecutive reads habits good:

$p = \frac{1}{5} \Rightarrow q = 1 - p = \frac{4}{5}p= 5 1 ​ ⇒q=1−p= 5 4$

Then, according to the Bernoulli formula, the wanted probability is

$P_{10}(2)=C _{10}^2p^2 q^8 =\frac{10!}{ 2!8!} (\frac{1}{5})^2(\frac{4}{5})^8=\frac{580824}{1953155}=0.301989888$