One card is drawn at random from a pack of well-shuffled deck of 52 cards. In which of the following cases are the events E and F are independent?
E : “the card drawn is a spade”
F : “the card drawn is an ace”.

Solution

P(E) = P(the card drawn is spade) = $13 over 52 space equals space 1 fourth$
P(F) = P (the card drawn is an ace) = $4 over 52 space equals 1 over 13$
$straight P left parenthesis straight E space intersection space straight F right parenthesis space equals space straight P left parenthesis card space drawn space is space straight a space spade space and space also space an space ace right parenthesis$
$equals space straight P left parenthesis card space drawn space is space an space ace space of space spade right parenthesis space equals space 1 over 52$
Now, $straight P left parenthesis straight E right parenthesis cross times straight P left parenthesis straight F right parenthesis space equals 1 fourth cross times 1 over 13 space equals 1 over 52$
$therefore space space space space straight P left parenthesis straight E space intersection space straight F right parenthesis space equals space straight P left parenthesis straight E right parenthesis space cross times space straight P left parenthesis straight F right parenthesis therefore space space space events space straight E space and space straight F space are space independent.$

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Probability

One card is drawn at random from a pack of well-shuffled deck of 52 cards. In which of the following cases are the events E and F are independent?
E : “the card drawn is a spade”
F : “the card drawn is an ace”.

Some More Questions From Probability Chapter

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Probability

One card is drawn at random from a pack of well-shuffled deck of 52 cards. In which of the following cases are the events E and F are independent?E : “the card drawn is a spade”F : “the card drawn is an ace”.

Some More Questions From Probability Chapter

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

One card is drawn at random from a pack of well-shuffled deck of 52 cards. In which of the following cases are the events E and F are independent?
E : “the card drawn is a spade”
F : “the card drawn is an ace”.