Question

a) If a single six-sided die is rolled five times, what is the probability that a 6 is thrown exactly three times?

b) A person receives an average of one e-mail message per half-hour interval. Assume that e-mails are received randomly in time, find the probabilities that in a particular hour 0,1,2,3,4,5 messages are received.

Answer 1

a) P(Getting 6 in any single throw) = 1/6

Hence,

P(Getting 6 three times in 5 throws)

= 0.03215

b) Average = 1 email per half hour = 2 emails per hour

Hence,

x	Probability calculation	Probability
0	$\frac{e^{-2}2^0}{0!}$	0.1353
1	$\frac{e^{-2}2^1}{1!}$	0.2707
2	$\frac{e^{-2}2^2}{2!}$	0.2707
3	$\frac{e^{-2}2^3}{3!}$	0.1804
4	$\frac{e^{-2}2^4}{4!}$	0.0902
5	$\frac{e^{-2}2^5}{5!}$	0.0361