1 statistics 2017 mid testpdf - Adobe Acrobat Reader DC — X

File Edit View Window Help Home Tools statistic52017 mid... >< statistic52017mid... ® 7311; ' [315159ng @© 2 I6 6/ Dirk likes having Lcoffee and biscuits everyday. Let X denote the number of cups of coffee

Dirk drinks on any given day. The number of cups of coffee Dirk drinks is independent

from day to day. Let Y denote the number of biscuits Dirk cats on any given day. The

number of biscuits Dirk eats is independent from day to day. The relationship between

X and Y is described by the following joint probability distribution: 3; (Biscuit)

3 4 6

0.12 0.25 0.04 I(Coffee) 0.14 0.20 0.02

0.10 0.05 0.08 (a) 3 marks] Find the probability that Dirk drank 3 cups of coffee today, given that

he ate more than 3 biscuits. Solution:

0.4531 (h) 3 marks] Find the probability that Dirk ate 3 biscuits today, given that he drank

more than 3 cups of coﬁee, Solution:

0,4068 (c) 4 marks] Over the next 10 days, ﬁnd the probability that Dirk drank more than

3 cups of coffee on more than 7 days. Solution:

0.1517 (d) 3 marks] Over the next 30 days, ﬁnd the probability that Dirk drank more than

3 cups of coffee on more than 20 days. Solution:

0.1977 10'"! PM E