One card is drawn from a well shuffled pack of 52 cards. If E is the event “the card drawn is a king or queen” and F is the event “the card drawn is a queen or an ace”, then find the probability of the conditional event E/F.

Solution

E : The card drawn is king or queen
F : The card drawn is queen or ace.
$straight E intersection straight F colon space The space card space drawn space is space queen$
$therefore space space space space space straight P left parenthesis straight E intersection straight F right parenthesis space equals space 4 over 52 space equals 1 over 13 space space space space space space space space space straight P left parenthesis straight F right parenthesis space equals 8 over 52 space equals space 2 over 13 therefore space space space space space straight P left parenthesis straight E divided by straight F right parenthesis space equals space fraction numerator straight P left parenthesis straight E intersection straight F right parenthesis over denominator straight P left parenthesis straight F right parenthesis end fraction space equals space fraction numerator begin display style 1 over 13 end style over denominator begin display style 2 over 13 end style end fraction space equals space 1 half.$

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Probability

One card is drawn from a well shuffled pack of 52 cards. If E is the event “the card drawn is a king or queen” and F is the event “the card drawn is a queen or an ace”, then find the probability of the conditional event E/F.

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