Q1. a) In a group of 80 students, 50 have a laptop (), 30 have a tablet () and 3 have both a laptop and a tablet.

i) Draw a Venn diagram to represent this information.

ii) Find the probability that a student either only has a tablet or does not have a laptop or both, using the equation ( ) = ( ) + () ( ) (5 marks) b) If () = 0.1 ( ) = 0.03 (|) = 0.2,

find the following probabilities:

i) Conditional probability of B if A has occurred, (|) (2 marks)

ii) The probability of B, ()

iii) The probability of , ( )

A law firm has determined that they win 73% of the cases they are involved in. This week, they are handling five different cases. Find the probability that

a) exactly four cases will be won

b) at least two cases will be won .