NCERT Class XII Mathematics Chapter - - Solutions
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Question : 32
Total: 101
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) 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’.
Solution:
(i) P ( E ) =
=
P ( F ) =
=
⇒ P ( E ∩ F ) =
=
×
= P ( E ) P ( F )
⇒ E and F are independent.
(i)P ( E ) =
=
P ( F ) =
=
⇒ P ( E ∩ F ) =
=
=
×
= P ( E ) P ( F )
⇒ E and F are independent.
(iii)P ( E ) =
+
=
P ( F ) =
+
=
⇒ P ( E ∩ F ) =
=
≠
×
⇒ P ( E ∩ F ) ≠ P ( E ) P ( F )
⇒ E and F are not independent.
⇒ E and F are independent.
(i)
⇒ E and F are independent.
(iii)
⇒ E and F are not independent.
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