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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?
(i) E: ‘the card drawn is a spade’
F: ‘the card drawn is an ace’
(ii) E: ‘the card drawn is black’
F: ‘the card drawn is a king’
(iii) E: ‘the card drawn is a king or queen’
F: ‘the card drawn is a queen or jack’
Asked by Nishit Last Modified
Answer 
Total cards=52 probability of getting space card p(E)=13/52=1/4 there are 4 aces in a deck of cards probability of getting a ace p(E)=4/52=1/13 there is only one card which is an ace ofspade =1/52 =p(E^F) =1/4×1/13=1/52=P(A)×P(B) event E and F are independent
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Vishaka Bhutia
Home Tutor
(i) In a deck of 52 cards, 13 cards are spades and 4 cards are aces.
∴ P(E) = P(the card drawn is a spade) =
∴ P(F) = P(the card drawn is an ace) =
In the deck of cards, only 1 card is an ace of spades.
P(EF) = P(the card drawn is spade and an ace) =
P(E) × P(F) =
⇒ P(E) × P(F) = P(EF)
Therefore, the events E and F are independent.
(ii) In a deck of 52 cards, 26 cards are black and 4 cards are kings.
∴ P(E) = P(the card drawn is black) =
∴ P(F) = P(the card drawn is a king) =
In the pack of 52 cards, 2 cards are black as well as kings.
∴ P (EF) = P(the card drawn is a black king) =
P(E) × P(F) =
Therefore, the given events E and F are independent.
(iii) In a deck of 52 cards, 4 cards are kings, 4 cards are queens, and 4 cards are jacks.
∴ P(E) = P(the card drawn is a king or a queen) =
∴ P(F) = P(the card drawn is a queen or a jack) =
There are 4 cards which are king or queen and queen or jack.
∴ P(EF) = P(the card drawn is a king or a queen, or queen or a jack)
=
P(E) × P(F) =
Therefore, the given events E and F are not independent.
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The probability of obtaining an even prime number on each die, when a pair of dice is rolled is
(A) 0 (B) 
(C) 
(D) 
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