Question

If a quarter is tossed five times and comes up tails twice and heads three times, the probability of heads on the next two tosses is ...

Answer #1

The probability of heads on the next two tosses is independent of everything that has happened(all the coin tosses) upto that point in time as consecutive coin tosses are independent of each other.

Considering the coin to be fair, the probabilty that the next two tosses will yield heads given that in the before 5 tosses we have got tails twice and heads three times is given by :

P(heads next two tosses / tails twice and heads three times in
previous 5 tosses) = P(heads next two tosses) = (1/2) * (1/2) =
**1/4**

This is because both the events are independent

If a penny is tossed three times and comes up heads all three
times, the probability of heads on the fourth trial is ___.
zero
1/16
½
larger than the probability of tails

A coin is tossed repeatedly until heads has occurred twice or
tails has occurred twice, whichever comes first. Let X be the
number of times the coin is tossed.
Find: a. E(X). b. Var(X).
The answers are 2.5 and 0.25

(a) A fair coin is tossed five times. Let E be the event that an
odd number of tails occurs, and let F be the event that the first
toss is tails. Are E and F independent?
(b) A fair coin is tossed twice. Let E be the event that the
first toss is heads, let F be the event that the second toss is
tails, and let G be the event that the tosses result in exactly one
heads...

If a coin is tossed 100 times, what is the probability that (a)
it comes up heads more than 60 times; (b) the observed proportion
of heads exceeds 0.6.

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 ∈...

A coin is tossed five times. By counting the elements in the
following events, determine the probability of each event. (Show
your work)
a. Heads never occurs twice in a row.
b. Neither heads or tails occur twice in a row
c. Both heads and tails occur at least twice in a row.
The answers are 13/32, 1/16, and 1/4. I'm just stuck on how to
get them.

A biased coin is tossed ten times. Given that exactly four Heads
were obtained, what is the conditional probability that exactly two
Heads were obtained in the first five tosses?

A fair coin is tossed three times. Let X be the number of heads
among the first two tosses and Y be the number of heads among the
last two tosses. What is the joint probability mass function of X
and Y? What are the marginal probability mass function of X and Y
i.e. p_X (x)and p_Y (y)? Find E(X) and E(Y). What is Cov(X,Y) What
is Corr (X,Y) Are X and Y independent? Explain. Find the
conditional probability mass...

A coin is tossed three times. An outcome is represented by a
string of the sort
HTT
(meaning heads on the first toss, followed by two tails).
The
8
outcomes are listed below. Assume that each outcome has the same
probability.
Complete the following. Write your answers as fractions.
(a)Check the outcomes for each of the three events below. Then,
enter the probability of each event.
Outcomes
Probability
HHH
HHT
HTH
HTT
THH
THT
TTH
TTT
Event A: Exactly two...

A coin is tossed 100 times and the results are recorded. 40
times the coin lands on heads, the other 60 times the coin lands on
tails. If 40 of the recorded tosses were selected at random, what
is the probability that the coin landed on heads exactly 14
times?

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