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JEE Advanced Model Paper 4 with solutions for online practice
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© examsnet.com
Question : 48
Total: 54
Which of the following statement(s) is/are correct?
3 coins are tossed once. Two of them atleast must land the same way. No matter whether they land heads or tails, the third coin is equally likely to land either the same way or oppositely. So, the chance that all the three coins land the same wayis
1
2
Let 0 < P (B) < 1 and P (A/B) = P (A/
B
C
) then A and Bare independent.
Suppose an urn contains w white and b black balls and a ball is drawnfrom it and is replaced along with d additional balls of the same colour.Now a second ball is drawn from it. The probability that the seconddrawn ball is white is independent of the value of d.
A man has ten keys only one of which fits the lock. He tries them in adoor one by one discarding the one he has tried. The probability that fifthkey fits the lock is
1
10
Validate
Solution:
(a) P
(
T
T
T
)
or P
(
H
H
H
)
P (TTT or HHH) =
1
8
+
1
8
=
1
4
Hence statement is false.
(b)
P
(
A
∩
B
)
P
(
A
)
-
P
(
A
∩
B
c
)
1
−
P
(
B
)
=
P
(
A
)
−
P
(
A
∩
B
)
1
−
P
(
B
)
[Note that probability of occcurrence.of.A is same whether B occurs or does notoccurs ⇒ A and B are independent]
P (A ∩ B) [1 - P(B)] = P(B)
P(A) - P(B) . P(A ∩ B)
P(A ∩ B) = P(A) . P(B)
⇒ true
P(W) =
w
w
+
d
.
w
+
d
w
+
d
+
b
+
b
b
+
w
.
w
w
+
b
+
d
=
w
(
b
+
w
)
(
w
+
b
+
d
)
(w + d + b)
w
w
+
b
Hence the probability that 2nd ball drawn is white is independent of d.
(d) Every key that fits have the same probability =
1
10
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