Q.15    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’

Answers (1)

One card is drawn at random from a well shuffled deck of 52 cards

Total ace = 4

total spades =13

E : ‘the card drawn is a spade

 F : ‘the card drawn is an ace’

P(E)=\frac{13}{52}=\frac{1}{4}

P(F)=\frac{4}{52}=\frac{1}{13}

E\cap F : a card which is spade and ace = 1

P(E\cap F)=\frac{1}{52}

P(E).P(F)=\frac{1}{4}\times \frac{1}{13}=\frac{1}{52}

\Rightarrow P(E\cap F)=P(E).P(F)=\frac{1}{52}

Hence, E and F are indepentdent events .

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