One card is drawn at random from a well shuffled deck of 52 cards. In which of the following cases are the events E and F independent? (i) E : the card drawn is a spade F : the card drawn is an ace (ii) E : the card drawn is black F : the card drawn in a king

Explanation

Correct option is A)
In a deck of 52 cards, 13 cards are spades and 4 cards are aces.

∴P(E)=P(the card drawn is a spade)=`13/52​=1/4`

∴P(F)=P(the card drawn is an ace)=`4/52​=1/13`​

In the deck of cards, only 1 card is an ace of spades.

P(EF)=P(the card drawn is spade and ace)=`1/52​`

`P(E)×P (F)=1/4*1/13​=1/52`

⇒`P(E)×P(F)=P(EF)`

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