Question

About ten percent of users do not close Windows properly. Suppose that Windows is installed in a public library that is used by random people in a random order. (a) On the average, how many users of this computer do not close Windows properly before someone does close it properly? (b) What is the probability that exactly 8 of the next 10 users will close Windows properly?

Answer 1

Answer:

See explanation

Step-by-step explanation:

Since about ten percent of users do not close Windows properly, we have

• the probability that a user does not close Windows properly is $p=0.1;$
• the probability that a user closes the Windows properly is $q=1-p=1-0.1=0.9.$

A. On the average,

• one of 10 users does not close the Windows properly;
• 10 of 100 users do not close Windows properly.

B. The probability that exactly 8 of the next 10 users will close Windows properly is

$C^{10}_8\cdot q^{8}p^{10-8}=\dfrac{10!}{8!(10-8)!}\cdot (0.9)^8\cdot (0.1)^2=45\cdot (0.9)^8\cdot (0.1)^2\approx 0.1937$