Question

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 black”,
F : “the card drawn is a king”.

Name: Wired Faculty - The Best Learning App
Rating: 4.6 (1864 reviews)

Solution

straight P left parenthesis straight E right parenthesis space equals space straight P space left parenthesis card space drawn space is space black right parenthesis space equals space 26 over 52 space equals space 1 half straight P left parenthesis straight F right parenthesis space equals space straight P left parenthesis card space drawn space is space straight a space king right parenthesis space equals 4 over 52 space equals space 1 over 13

straight P left parenthesis straight E intersection straight F right parenthesis space equals space straight P left parenthesis card space drawn space is space black space and space card space drawn space is space king right parenthesis space space space space space space space space space space space space space space space space equals space straight P left parenthesis card space drawn space is space straight a space black space king right parenthesis space equals space 2 over 52 space equals 1 over 26

Now, P(E) x P(F) =

1 half cross times 1 over 13 equals space 1 over 26

therefore space space space straight P left parenthesis straight E intersection 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. space

For Daily Free Study Material Join wiredfaculty