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 ?

                (ii) E : ‘the card drawn is black’

                     F : ‘the card drawn is a king’

            

Answers (1)

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

Total black card = 26

total king =4

E : ‘the card drawn is black’

 F : ‘the card drawn is a king’

P(E)=\frac{26}{52}=\frac{1}{2}

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

E\cap F : a card which is black and king = 2

P(E\cap F)=\frac{2}{52}=\frac{1}{26}

P(E).P(F)=\frac{1}{2}\times \frac{1}{13}=\frac{1}{26}

\Rightarrow P(E\cap F)=P(E).P(F)=\frac{1}{26}

Hence, E and F are indepentdent events .

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