Question

If you flip a fair coin and get heads 10 times in a row, what is the chance of getting tails on the next flip? Explain.

Answer #1

There is an 1/2 chance to get a head of a coin each time. To get 10 heads in a row, an 1/2 chance has to be multiplied for 10 times. So, the formula to complete the coin scam on the first attempt is (1/2)10. As a result, the chance of DB completing the coin scam on the first attempt is 1/1024.

The grey traces (representing nH−nT) are a Bernoulli random walk. If you think of a particle moving up or down the y-axis by a unit step (randomly with equal probability) at each time-step, then the distribution of the position of the particle will 'diffuse' away from 0 over time.

nH-nT=0.5

10-nT=0.5

T=10.5/11

=0.9545

The chance of getting tails on the next flip is 0.9545.

i
flip one fair coin until I get 4 tails( total, not in a row) or 3
heads ( total, not in a row).
(a) what is the maximum number of flips for this game?
(b) what is the probability the game requires exactly 4
flips?
(c) what is the probability the 3 heads occur before the 4
tails?
(d) what is the probability if I filp 10 fair cions at least 8
are heads?

You flip a fair coin. If the coin lands heads, you roll a fair
six-sided die 100 times. If the coin lands tails, you roll the die
101 times. Let X be 1 if the coin lands heads and 0 if the coin
lands tails. Let Y be the total number of times that you roll a 6.
Find P (X=1|Y =15) /P (X=0|Y =15) .

You are flipping a fair coin with one side heads, and the other
tails. You flip it 30 times.
a) What probability distribution would the above most closely
resemble?
b) If 8 out of 30 flips were heads, what is the probability of
the next flip coming up heads?
c) What is the probability that out of 30 flips, not more than
15 come up heads?
d) What is the probability that at least 15 out 30 flips are
heads?...

Flip a fair coin 10 times. What is the probability of getting at
least 7 tails?
0.171875
0.192321
0.141772
0.166187

Suppose you toss a coin 100 times. Should you expect to get exactly
50 heads? Why or why not?
A. Yes, because the number of tosses is even, so if the coin
is fair, half of the results should be heads.
B. No, because the chance of heads or tails is the same, the
chance of any number of heads is the same.
C. No, there will be small deviations by chance, but if the
coin is fair, the result...

If you flip a coin 56 times, how many times would you expect to
get either 3 heads or 3 tails?

Suppose you flip a fair coin 10 times. What is the
probability of the last two flips both being heads if you know that
the first eight flips were heads?

You flip a coin until getting heads. Let X be the number of coin
flips.
a. What is the probability that you flip the coin at least 8
times?
b. What is the probability that you flip the coin at least 8
times given that the first, third, and fifth flips were all
tails?
c. You flip three coins. Let X be the total number of heads. You
then roll X standard dice. Let Y be the sum of those...

If you flip a fair coin 6 times, find the probability of
having
a.) exactly one head
b.)more than one head
c.)same number of heads and tails
d.)more heads than tails

Suppose you flip a fair coin six times where A is the number of
tails and B is the number of heads. Prove if E(X*Y) is not equal to
E(X)E(Y).

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