Question

REPOST: A biased coin has 0.75 probability of flipping heads and 0.25 of flipping tails. What is the probability that the sequence TTHH (T=tails, H=heads) only occurs after the 8th flip?

Answer #1

**Given:-**

P(Flipping Heads) = 0.75

P(Flipping Tails) = 0.25

We have to find the probability:

**P(TTHH only occurs after the 8th flip) = 1 - P(TTHH
occurs before the 8th flip)**

Now

P(TTHH occurs before the 8th flip) = P(TTHHXXXX)+ P(XTTHHXXX) + P(XXTTHHXX) + P(XXXTTHHX)+ P(XXXXTTHH)

Here X can be either heads or tails

=
(0.75)^{2}*(0.25)^{2}*(((0.75)^{0}*(0.25)^{4}*1+(0.75)^{1}*(0.25)^{3}*4+(0.75)^{2}*(0.25)^{2}*6+(0.75)^{3}*(0.25)^{1}*4+(0.75)^{4}*(0.25)^{0}*1)*5

**= 0.17578125**

Therefore

**P(TTHH only occurs after the 8th flip) = 1 - P(TTHH
occurs before the 8th flip) =** 1 - 0.17578125 **=
0.82421875**

A selection of coin is known to be either fair (with a
probability 0.5 of coming up heads or tails when flipped) or biased
(with a probability 0.75 of tails, 0.25 of heads.) Further. it is
known that 1/10 of the coins are biased. a) You select a coin at
random. What are the prior odds (not probability) that you have
picked a biased coin? b) You select a coin at random and flip it;
you get tails. What are...

In a situation where we have a biased coin that is tails with
probability 0.7 and we independently flip it 10 times. Find the
following probabilities.
1. getting the sequence HTHHHTHTTH?
2. exactly 4 tails?
3. at least 4 tails?
4. expected number of tails? expected number of heads?

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?

I toss a biased coin 15 times, with a probability of heads: ? =
0.25. Let x equal the number of heads I toss. The probability I
toss at least 2 heads is _________________ (3 points)

Suppose you and your roommate use a coin-flipping app to decide
who has to take out the trash: heads you take out the trash, tails
your roommate does. After losing a number of flips, you start to
wonder if the coin-flipping app really is totally random, or if it
is biased in one direction or the other.
To be fair to your roommate, you wish to test whether the app is
biased in either direction, and thus a two-tailed test...

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 weighted coin has probability 0.7 of getting heads, and 0.3 of
getting a tails. If the coin is tossed 6 times, what is the
probability of getting at least 4 heads? What is the probability of
getting less than 4 heads?

What is the probability of flipping a coin and hitting
heads in 8 out of 11 tries?

A box contains 4 coins: coin1 has both sides tails; coin2 has
both sides heads; coin3 has both sides heads; coin4 is a regular
coin (one side heads, one side tails)
a) If we randomly choose one coin from the box and flip, what is
the probability we get heads?
b) Suppose we randomly choose a coin, flip, and get heads. What
is the probability that the coin that was chosen is the regular
coin?

What is the probability percentage of flipping a coin 30 times
and landing heads all 30 times.

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 2 minutes ago

asked 6 minutes ago

asked 6 minutes ago

asked 7 minutes ago

asked 8 minutes ago

asked 15 minutes ago

asked 15 minutes ago

asked 17 minutes ago

asked 22 minutes ago

asked 33 minutes ago

asked 36 minutes ago

asked 37 minutes ago