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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? (iii) E: 'the card drawn is a king or queen'

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 ?

                (iii) E : ‘the card drawn is a king or queen’

                     F : ‘the card drawn is a queen or jack’.

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

Total king or queen = 8

total queen or jack = 8

E : ‘the card drawn is a king or queen’

F : ‘the card drawn is a queen or jack’.

P(E)=\frac{8}{52}=\frac{2}{13}

P(F)=\frac{8}{52}=\frac{2}{13}

E\cap F : a card which is queen  = 4

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

P(E).P(F)=\frac{2}{13}\times \frac{2}{13}=\frac{4}{169}

\Rightarrow P(E\cap F)\neq P(E).P(F)

Hence, E and F are not indepentdent  events .

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