Question

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

Answer 1

option B (28/52)

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)