NCERT Class XII Mathematics Chapter - - Solutions
© examsnet.com
Question : 21
Total: 101
A fair coin and an unbiased die are tossed. Let A be the event ‘head appears on the coin’ and B be the event ‘3 on the die’. Check whether A and B are independent events or not ?
Solution:
Let S be the sample space of the given experiment S = { ( H , 1 ) , ( H , 2 ) , ( H , 3 ) , ( H , 4 ) , ( H , 5 ) , ( H , 6 ) , ( T , 1 ) , ( T , 2 ) , ( T , 3 ) , ( T , 4 ) , ( T , 5 ) , ( T , 6 ) }
⇒ A = {(H, 1), (H, 2), (H, 3), (H, 4), (H, 5), (H, 6)} and B : ‘3 appears on the die’
⇒ B = {(H, 3), (T, 3)} ⇒ A ∩ B = {(H, 3)}
Hence,P ( A ) =
=
, P ( B ) =
=
P ( A ∩ B ) =
P ( A ) × P ( B ) =
×
=
= P ( A ∩ B )
Hence, A and B are independent.
⇒ A = {(H, 1), (H, 2), (H, 3), (H, 4), (H, 5), (H, 6)} and B : ‘3 appears on the die’
⇒ B = {(H, 3), (T, 3)} ⇒ A ∩ B = {(H, 3)}
Hence,
Hence, A and B are independent.
© examsnet.com
Go to Question: