A magician has a collection of 52 cards, with 26 red and 26 black cards. Four of these cards are classified as 'special', and two of the special cards are red. If a card is chosen at random from the 52 cards, what is the probability that the card is special or red? Select one:

a. 2/52

b. 28/52

c. 26/52

d. 4/52

option B (28/52)

Step-by-step explanation:

from probability

P (A∪B) = P (A) + P (B) - P (A∩B)

where

P (A∪B) = probability that event A or B happen

P (A∩B) = probability that event A and B happen simultaneously

P (A) = probability that event A happen

P (B) = probability that event B happen

the probability that the card is special or red

P (special or red) = P (special) + P (red) - P (special and red)

since

P (special) = 4/52

P (red) = 26/52

P (special and red) = 2/52

therefore

P (special or red) = 4/52 + 26/52 - 2/52 = 28/52

P (special or red) = 28/52

(option B)