Question

One card is drawn at random from a well shuffled deck of 52 cards. Are E and F independent if E : the card drawn is black F : the card drawn is a king?

Answer 1

Answer:

E : the card drawn is black

F : the card drawn is a king

In a deck there are 52 cards - 26 of each color and and there are 4 kings, one in each suit, and 2 of each color.

Given E: the card drawn is black, P(E) = 26/52 = 1/2

Given F: the card drawn is a king, P(F) = 4/52 = 1/13

P (black card ∩ king ) = P (E ∩ F) = P (drawing an black king) = 2/52=1/26

Now, P (E ∩ F) = P(E) × P(F) = 1/2 × 1/13=1/26

Therefore E and F are independent.

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