NCERT Solutions
Class 12 Maths
Probability

Ex.13.2 Q.15
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’
(i) In a deck of 52 cards, 13 cards are spades and 4 cards are aces.
So, P(E) = P(the card drawn is a spade) =
And 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) =
Now,
=> 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.
So, P(E) = P(the card drawn is black) =
And P(F) = P(the card drawn is a king) =
In the pack of 52 cards, 2 cards are black as well as kings.
So, P(EF) = P(the card drawn is a black king) =
Now,
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.
So, 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.
So, P(EF) = P(the card drawn is a king or a queen, or queen or a jack) =
Now,
So, P(E) * P(F) ≠ P(EF)
Therefore, the given events E and F are not independent.