Question

question 3.

A coin has two sides, Heads and Tails. When flipped it comes up Heads with an unknown probability p and Tails with probability q = 1−p. Let ˆp be the proportion of times it comes up Heads after n flips. Using Normal approximation, find n so that |p−pˆ| ≤ 0.01 with probability approximately 95% (regardless of the actual value of p). You may use the following facts: Φ(−2, 2) = 95% pq ≤ 1/4 for any p ∈ [0, 1].

Answer #1

A coin with two sides, heads and tails, is flipped 100 times.
What is the probability that a "heads" will come up exactly 60
times?
Submit your answer as a decimal fraction (range: 0 to
1) to five (5) decimal places.

Suppose that an unfair coin comes up heads 52.2% of the time.
The coin is flipped a total of 19 times.
a) What is the probability that you get exactly 9 tails?
b) What is the probability that you get at most 17 heads?

When coin 1 is flipped, it lands on heads with probability
3
5
; when coin 2 is flipped it lands on heads with probability
4
5
.
(a)
If coin 1 is flipped 11 times, find the probability that it
lands on heads at least 9 times.
(b)
If one of the coins is randomly selected and flipped 10 times,
what is the probability that it lands on heads exactly 7
times?
(c)
In part (b), given that the...

A coin having probability p of coming up heads is successively
flipped until two of the most recent three flips are heads. Let N
denote the number of flips. (Note that if the first two flips are
heads, then N = 2.) Find E[N]. (please do not just copy the answer
from other solutions, I need a thoroughly explained answer)

When coin 1 is flipped, it lands on heads with probability
3/5 ; when coin 2 is flipped it lands on heads with probability
4/5 .
(a)
If coin 1 is flipped 12 times, find the probability that it
lands on heads at least 10 times.
(b)
If one of the coins is randomly selected and flipped 10 times,
what is the probability that it lands on heads exactly 7
times?
(c)
In part (b), given that the first of...

A biased coin has probability p to land heads and q = 1 − p to
land tails. The coin is flipped until the first occurrence that
differs from the initial flip. What is the number of flips
required, on average?

coin 1 has probability 0.7 of coming up heads, and coin 2 has
probability of 0.6 of coming up heads. we flip a coin each day. if
the coin flipped today comes up head, then we select coin 1 to flip
tomorrow, and if it comes up tail, then we select coin 2 to flip
tomorrow. find the following:
a) the transition probability matrix P
b) in a long run, what percentage of the results are heads?
c) if the...

A fair coin is flipped six times. Find the probability that
heads comes up exactly four times.
1/16
15/64
90/16
1/4
2/3

Deriving fair coin flips from biased coins: From coins with
uneven heads/tails probabilities construct an experiment for which
there are two disjoint events, with equal probabilities, that we
call "heads" and "tails".
a. given c1 and c2, where c1 lands heads up with probability 2/3
and c2 lands heads up with probability 1/4, construct a "fair coin
flip" experiment.
b. given one coin with unknown probability p of landing heads
up, where 0 < p < 1, construct a "fair...

Suppose Tori has an unfair coin which lands on Tails with
probability 0.28 when flipped. If she flips the coin 10 times, find
each of the following:
The mean number of Tails
P(Less than or equal to 2 Tails)
P(No more than 3 Tails)
P(No Tails)
P(At least 1 Tail)
P(Exactly 1 Tail)
P(Exactly 4 Tails)
P(At least 5 Tails)
P(More than 3 Tails)
The standard deviation of the number of Tails
1.
0.1798
2.
0.7021
3.
2.8
4.
0.1181...

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