A standard deck of cards contains 52 cards One card is selec

A standard deck of cards contains 52 cards. One card is selected from the deeck.

a) compute the probability of randomly sselecting a heart or diamond.

b) Compute the probability of randomly selecting a heart orr diamond or club.

c) Compute the probability of raqndomly selecting a ace or spade.

a) P(heart or diamond)= (Type an integer or a simplified fraction.)

b)P(heart of diamond or club)= (Type an integer or a simplified fraction.)

c) P(ace or spade)= (type an integer or a simplified fraction.)

Solution

Given One card is selected from the deck of 52 cards

a) P(heart or diamond) = P(heart) + P(diamond) - P(heart and diamond)

                                     = (13c₁ / 52c₁) + (13c₁ / 52c₁) - 0

                                      = 26 / 52 = 0.5

b) P(heart or diamond or club) = P(heart) + P(diamond) + P(club) - P(heart and diamond) - P(heart and club)

                                                    - P((club and diamond) + P(heart and diamond and club)

                                   = (13c₁ / 52c₁) + (13c₁ / 52c₁) +(13c₁ / 52c₁) - 0 - 0 - 0 + 0

                                                 = 39 / 52 = 0.75

c) P(ace or Spade) = P(ace) + P(spade) - P(ace and space)

                              = (4c₁ / 52c₁) + (13c₁ / 52c₁) - (1c₁ / 52c₁)

                              = 16 / 52

                              =0.3077