A car dealership sells electric, hybrid, and petrol-fuelled vehicles. Vehicles may have automatic or manual transmission, and they come in two sizes: compact or large. Some vehicles have inbuilt sat-navs, and some have bluetooth capability. Vehicles come in a variety of colours, but most of the ones in the dealership are white or silver.

Define events E, H, and P for the three fuel types; A and M for the transmission types; C and L for the two sizes; N and B for sat-nav and bluetooth features; and W and S for white and silver colours.

a. What sample space are we implicitly assuming when we define these events?

b. Say whether or not the following events form a partition of the sample space. If they don’t, explain why.

i. E, H, and P.

ii. A and M.

iii. C and L.

iv. N and B.

v. W and S.

c. Say whether or not the following events form a partition of the stated event. If they don’t, explain why.
i. C and L for W.
ii. C ∩ W and L ∩ W for W.
iii. N and B for N ∪ B.
iv. W and S for W ∪ S.
v. A ∩ P and M ∩ P for P.