If one card is drawn from an ordinary deck of card, find the probability of having:

Question

a.) a king or a queen or a jack

b.) a club or heart or spade

c.) a king or a queen or a diamond

d.) an ace or diamond or a heart

e.) a 9 or 10 or a spade or a club

Answer 1

There are 52 cards in a deck

a) there are 12 face cards. the probability of a face card is 12/52

b) there are 13 clubs, 13 hearts and 13 spades so 39 cards wil be one of these. the prob is 39/52

c) this is getting a bit trickier we have to make sure we don't double count. 13 cards are diamonds of which one is a king and one is a queen. there are three kings and 3 queens which aren't diamonds so we could pick 13 cards that are diamonds c queens that arent diamonds and 3 kings that arent diamonds or 19 cards the prob is 19/52

d)similar to c) 26 cards are either diamonds or hearts. and there are two aces that are neither diamonds or hearts. so here, the Probability is (26+2)/52 or 28/52

e)Similar to c and d. there are 26 black cards. plus there are 2 9's and 2 10's which aren't black. so there are 30 ways to have this outcome. the prob is 30/52.

Hope this helps

Lenny