Total numbers of elementary events are: 52

(i) Let E be the event of drawing a card of spade or an ace

Let A be the event of drawing a card of spade

The favourable numbers of drawing a card of spade are: 13

P (spade) = P (E) = 13/52

Let B be the event of drawing an ace

The numbers of favourable outcomes are: 3 one ace being spade card already been counted

P (ace) = P (B) = 3/52

∴ P (spade or ace) = P (E) = P (A) + P(B) = 13/52 + 3/52 = 16/52 = 8/26 =4/13

(ii) Let E be the event of drawing a red king

The numbers of favourable outcomes are: 2

∴ P (red king) = P (E) = 2/52 = 1/26

(iii) Let E be the event of drawing either a king or a queen

Let A be the event of drawing a king

Then, the numbers of favourable outcome are: 4

P (king) = P (A) = 4/52

Let B be the event of drawing a queen

Then, the numbers of favourable outcome are: 4

P (queen) = P (B) = 4/52

∴ P (king or queen) = 4/52 + 4/52 = 8/52 = 2/13 -----@

(iv) Let E be the event of drawing neither a king nor a queen

P (getting either king or a queen) = 2/13 (part c above ----@)

∴ P (neither king nor queen) = P (E) = 1 – P (either king or queen) = 1 – 2/13 = 11/13