Question

an old modem can take anywhere from 0 to 30 seconds to establish a connection, with all times between 0 and 30 being equally likely. a. what is the probability that if you use this modem you will have to wait more than 15 seconds to connect? b. given that you have already waited 10 seconds, what is the probability of having to wait at least 10 more seconds?

Answer 1

The probability to wait more than 15 seconds to connect is 50% and the probability to wait at least 10 more seconds after waiting 10 seconds is 33.33%.

How to calculate the probability?

x = old modem establish connection = [0, 30]

Probability density function or PDF is

f(x) = $\frac{1}{b-a}$; 0 ≤ x ≤ 30

Probability to wait more than 15 seconds to connect is

f(X>5) = $\int\limits^{30}_{15} {f(x)} \, dx$

= $\int\limits^{30}_{15} {\frac{1}{b-a}} \, dx$

= $\frac{1}{30-0} \, [x]^{30}_{15}$

= $\frac{30-15}{30}$

= 0.5 or 50%

Probability if already waited 10 seconds and having to wait at least 10 more seconds is equal to wait at least 20 seconds from start. So,

f(X>5) = $\int\limits^{30}_{20} {f(x)} \, dx$

= $\int\limits^{30}_{20} {\frac{1}{b-a}} \, dx$

= $\frac{1}{30-0} \, [x]^{30}_{20}$

= $\frac{30-20}{30}$

= 0.3333 or 33.33%

Thus, the 50% probability to wait more than 15 seconds to connect and 33.33% probability to wait at least 20 seconds to connect.

Learn more about probability here:

brainly.com/question/29487191

#SPJ4