Question

A card is selected from a regular deck of cards.  Count the number of outcomes with:  a) a king or a queen, b) red and ace, c) spade and heart, and d) odd or less than five.

Answer 1

Given that 1 single card is selected from a deck of 52 cards.

a) to find the number of outcomes with a king or a queen

total number of king =4

total number of queen =4

So total number of outcome is = 4+4=8

b) total number of aces are 4 and out of those 4 only 2 are red

so total number of favourable outcome=2

c) Spade and heart

It is known that there are 13 spade cards and 13 heart cards but there is no card which is both a spade as well as a heart

Hence the total number of favourable outcomes =0.

d) Odd or less than five

Here the odd cards would be 3,5,7,9

And the total number of these cards are equal to =16 (4 from each suit).

Total number of cards less than 5 can be 2,3,4

But we have already considered 3 in the odd scenario

Hence the total number of cards less than 5 are = 8 (2 from each suit)

Hence the total number of favourable outcomes are =16+8=24.

Thank you !!!