Question

a card is randomly selected from a standard deck of 52 cards find the probability of drawing a spade or a club and a 6 and a face card

Answer 1

Could you be more specific? Is it the probability of drawing a spade OR a club, then of drawing a 6 AND a face?

Answer 2

The probability of drawing a spade OR a club and drawing a 6 AND a face

Answer 3

Okay, using the inclusion/exclusion principle, and letting \(S,C,6,F\) denote the event that you draw a spade, club, 6, or face (respectively),
\[P(S\cup C)=P(S)+P(C)-P(S\cap C)\]
\(P(S\cap C)=0\), since no card can be both a spades AND a club.

The second probability, \(P(6\cap F)\), is 0 because no card can be a 6 AND a face card at the same time.