MathDB
Problems
Contests
National and Regional Contests
India Contests
India LIMIT
2020 LIMIT
2020 LIMIT Category 2
19
19
Part of
2020 LIMIT Category 2
Problems
(1)
limit of probability , first n tosses of unbiased coin
Source: LIMIT 2020 Cat 2 Objective P19
6/9/2020
Consider an unbiased coin which is tossed infinitely many times. Let
A
n
A_n
A
n
be the event that no two successive heads occur in the first
n
n
n
tosses of this experiment. Then which of the following is incorrect : (A)
lim
n
→
∞
P
(
A
n
)
=
0
\lim_{n \to \infty} P(A_n)=0
lim
n
→
∞
P
(
A
n
)
=
0
(B)
lim
n
→
∞
3
n
P
(
A
n
)
=
0
\lim_{n \to \infty}3^n P(A_n)=0
lim
n
→
∞
3
n
P
(
A
n
)
=
0
(C)
2
n
P
(
A
n
)
+
2
n
+
1
P
(
A
n
+
1
)
=
2
n
+
2
P
(
A
n
+
2
2^nP(A_n) +2^{n+1}P(A_{n+1})=2^{n+2}P(A_{n+2}
2
n
P
(
A
n
)
+
2
n
+
1
P
(
A
n
+
1
)
=
2
n
+
2
P
(
A
n
+
2
(D)
lim
n
→
∞
P
(
A
n
)
P
(
A
n
+
1
)
\lim_{n \to \infty} \frac{P(A_n)}{P(A_{n+1})}
lim
n
→
∞
P
(
A
n
+
1
)
P
(
A
n
)
is lesser than
1.2
1.2
1.2
probability
limti
calculus