NCERT Class XII Mathematics Chapter - - Solutions
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Question : 22
Total: 101
A die marked 1, 2, 3 in red and 4, 5, 6 in green is tossed. Let A be the event, ‘the number is even’ and B be the event, ‘the number is red’. Are A and B independent ?
Solution:
The sample space is S = {1, 2, 3, 4, 5, 6}.
Given that A : ‘number is even’ ⇒ A = {2, 4, 6} and B : ‘number is red’
⇒ B = {1, 2, 3} ⇒ A ∩ B = {2}.
Now,P ( A ) =
=
P ( B ) =
=
P ( A ∩ B ) =
⇒ P ( A ∩ B ) ≠ P ( A ) P ( B ) ( ∵
≠
.
)
⇒ A and B are not independent.
Given that A : ‘number is even’ ⇒ A = {2, 4, 6} and B : ‘number is red’
⇒ B = {1, 2, 3} ⇒ A ∩ B = {2}.
Now,
⇒ A and B are not independent.
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