A card is selected from a standard deck of 52 playing cards. Find the probability of selecting
1. a five given the card is a not a club.
Since you are given that it is not a club, then you are drawing from a deck of
only 39 cards with no clubs, just hearts, diamonds and spades. In such a deck,
there are 3 fives. That's 3 out of 39, so the probability is or
reducing you get .
2. a heart given the card is red.
Since you are given that it is red, then you are drawing from a deck of only 26
cards with no spades or clubs, just hearts and diamonds. In such a deck,
there are 2 fives. That's 2 out of 26, so the probability is or
reducing you get .
3. a face card, given that the card is black. (An ace is not a face card.)
Since you are given that it is black, then you are drawing from a deck of only
26 cards with no hearts or diamonds, just spades and clubs. In such a deck,
there are 6 face cards, the J,Q and K of spades and the J,Q, and K of clubs.
That's 6 out of 26, so the probability is or reducing you get
.
Edwin