Question

Given a fair coin, if the coin is flipped n times, what is the probability that heads is only tossed on odd numbered tosses. (tails could also be tossed on odd numbered tosses)

Answer #1

According to the question, if Head comes, it will appear on 1st, 3rd, 5th....tosses.

But it’s not strictly given that on odd tosses, only Head can
appear. Which means, on even tosses only Tail can appear however in
odd tosses, both Head and tail can appear. So main restriction is
on even no of tosses. Now if n is even, there must be (n/2) even
places and if n is odd, there will be (n-1)/2 even places. So P(H
is only tossed in odd no of tosses) = (P(T))n/2 if n is even =
**(0.5)n/2, if n is even**

= (P(T))(n-1)/2 if n is odd = **(0.5)(n-1)/2. , if n is
odd.**

Suppose a fair coin is flipped three times.
A). What is the probability that the second flip is heads?
B). What is the probability that there is at least two
tails?
C). What is the probability that there is at most two heads?

A fair coin is tossed for n times independently. (i) Suppose
that n = 3. Given the appearance of successive heads, what is the
conditional probability that successive tails never appear? (ii)
Let X denote the probability that successive heads never appear.
Find an explicit formula for X. (iii) Let Y denote the conditional
probability that successive heads appear, given no successive heads
are observed in the first n − 1 tosses. What is the limit of Y as n...

3. A fair coin is flipped 4 times.
(a) What is the probability that the third flip is tails?
(b) What is the probability that we never get the same outcome
(heads or tails) twice in a row?
(c) What is the probability of tails appearing on at most one of
the four flips?
(d) What is the probability of tails appearing on either the
first or the last flip (or both)?
(e) What is the probability of tails appearing...

(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...

4. A fair coin is flipped 6 times.
a. what is the distribution
of outcomes?
b. what is the probability
of getting 4 heads/2 two tails in six flips of a
coin?

If a fair coin is flipped 120 times, what is the probability
that:
The number of heads is more than 70
The number of heads between 50 and 70?

A fair coin is tossed 9 times. left parenthesis Upper A right
parenthesis What is the probability of tossing a tail on the 9 th
?toss, given that the preceding 8 tosses were heads?? left
parenthesis Upper B right parenthesis What is the probability of
getting either 9 heads or 9 ?tails?

A coin is flipped 8 times. What is the probability that both
heads and tails occur?

A fair coin is tossed 4 times.
What is the probability of getting exactly 3 heads conditioned
on the event that the first two tosses came out the same?

PROBABILITY QUESTION
A fair coin is tossed n times. Sn is the # of heads
after tossed. Show that P(Sn ≥ 3n/4) ≤ e -n/8
.

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