Question

if one card is drawn from an ordinary deck of card, find the probability of getting each event. a. a 7 or an 8 or a 9, b. a spade or a queen or a king, c. a club or a fade card, d. an ace or a diamond or a heart, e. a 9 or a 10 or a spade or a club

Answer 1

a) P(7 or 8 ) = P(7) + P(8)

                    = 4/52 + 4/52 = 8/52 = 2/13 = 0.1538

b) P(spade or queen or king) = P(spade) + P(queen) + P(king) - P(spade and queen) - P(spade and king) - P(queen and king) + P(spade and queen and king)

= 13/52 + 4/52 + 4/52 - 1/52 - 1/52 - 0 + 0 = 19/52 = 0.3654

c) P(club or a face card) = P(club) + P(face card) - P(club and face card)

                                        = 13/52 + 12/52 - 3/52 = 22/52 = 0.4231

d) P(ace or diamond or heart) = P(ace) + P(diamond) + P(heart) - P(ace and diamond) - P(diamond and heart) - P(ace and heart) + P(ace and diamond and heart)

= 4/52 + 13/52 + 13/52 - 1/52 - 0 - 1/52 + 0 = 28/52 = 0.5385

e) P(9 or 10 or spade or club) = P(9) + P(10) + P(spade) + P(club) - P(9 and spade) - P(9 and club) - P(10 and spade) - P(10 and club)

   = 4/52 + 4/52 + 13/52 + 13/52 - 1/52 - 1/52 - 1/52 - 1/52

= 30/52 = 0.5769