Answer to Question #342842 in Statistics and Probability for JAYZ

Question

As urvey unofficially claimed that in every five young executives, only one practices good reading habits.

What is the probability that out of 10 young executives, two executives practice good reading habits? （b) What is the probability that at least five out of 20 young executives practice good reading habits? 

Answer 1

$P(x)=\frac {n!} {(n-x)!x!}p^xq^{n-x}$

where $p=1/5,q=1-p=4/5$

So,

a) $n=10$

$P(2)=\frac {10!} {(10-2)!2!}(\frac 1 5)^2(\frac 4 5 )^{10-2}=1.8*0.168=0.302=30.2\%$

b) $n=20$

$P(\ge5)=1-P(<5)=1-P(=0)-P(=1)-P(=2)-P(=3)-P(=4)$

$=1-\frac {20!} {(20-0)!0!}(\frac 1 5)^0(\frac 4 5 )^{20-0}-\frac {20!} {(20-1)!1!}(\frac 1 5)^1(\frac 4 5 )^{20-1}-\frac {20!} {(20-2)!2!}(\frac 1 5)^2(\frac 4 5 )^{20-2}-\frac {20!} {(20-3)!3!}(\frac 1 5)^3(\frac 4 5 )^{20-3}-\frac {20!} {(20-4)!4!}(\frac 1 5)^4(\frac 4 5 )^{20-4}=$

$=1-0.0115-0.0576-0.137-0.205-0.218=0.3709=37.9\%$