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Probability

Question
CBSEENMA12033661
Wired Faculty App

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 king or queen”
F : “the card drawn is a queen or jack”.

Solution

P(E) = P (card drawn is a king or queen) = 8 over 52 space equals 2 over 13
P(F) = P (card drawn is queen or jack) = 8 over 52 space equals space 2 over 13
straight P left parenthesis straight E intersection straight F right parenthesis space equals space straight P left parenthesis apostrophe card space drawn space is space straight a space king space or space queen apostrophe space and space apostrophe card apostrophe space drawn space is space straight a space queen space or space jack apostrophe right parenthesis
               space equals space straight P left parenthesis card space drawn space is space straight a space queen right parenthesis space equals 4 over 52 space equals space 1 over 13
straight P left parenthesis straight E right parenthesis space cross times space straight P left parenthesis straight F right parenthesis space equals space 2 over 13 cross times 2 over 13 space equals space 4 over 169 not equal to 1 over 13
therefore space space space space straight P left parenthesis straight E intersection straight F right parenthesis space not equal to space straight P left parenthesis straight E right parenthesis 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 not space independent.

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