Question

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 dice. What is P(X = 1|Y = 3)?

Answer #1

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 repeatedly flip a coin, whose probability of heads is p =
0.6, until getting a head immediately followed by a tail. Find the
expected number of flips you need to do.

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?...

suppose you flip a biased coin ( P(H) = 0.4) three times. Let X
denote the number of heads on the first two flips, and let Y denote
the number of heads on the last two flips. (a) Give the joint
probability mass function for X and Y (b) Are X and Y independent?
Provide evidence. (c)what is Px|y(0|1)? (d) Find Px+y(1).

flip a coin 10 times. find the probability of getting
tails in the first four flips.

Question 3: You are
given a fair coin. You flip this coin twice; the two flips are
independent. For each heads, you win 3 dollars, whereas for each
tails, you lose 2 dollars. Consider the random variable
X = the amount of money that you
win.
– Use the definition of expected value
to determine E(X).
– Use the linearity of expectation to
determineE(X).
You flip this coin 99 times; these
flips are mutually independent. For each heads, you win...

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?

Suppose Brian flips three fair coins, and let X be the number of
heads showing. Suppose Maria flips five fair coins, and let Y be
the number of heads showing. Let
Z = (X − Y) Compute P( Z = z)
.

An unfair coin is such that on any given toss, the probability
of getting heads is 0.6 and the probability of getting tails is
0.4. The coin is tossed 8 times. Let the random variable X be the
number of times heads is tossed.
1. Find P(X=5).
2. Find P(X≥3).
3. What is the expected value for this random variable?
E(X) =
4. What is the standard deviation for this random variable? (Give
your answer to 3 decimal places)
SD(X)...

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...

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