You toss a biased coin with the probability of heads as p. (a)
What is the...
You toss a biased coin with the probability of heads as p. (a)
What is the expected number of tosses required until you obtain two
consecutive heads ? (b) Compute the value in part (a) for p = 1/2
and p = 1/4.
A biased coin has probability of p =0.52 for heads. What is the
minimum number of coin tosses needed such that there will be more
heads than tails with 99% probability.
Suppose you flip a biased coin (that lands heads with
probability p) until 2 heads appear. Let X be the number of flips
needed for this two happen. Let Y be the number of flips needed for
the first head to appear. Find a general expression for the
condition probability mass function pY |X(i|n) when n ≥ 2.
Interpret your answer, i.e., if the number of flips required for 2
heads to appear is n, what can you say about...
There is a fair coin and a biased coin that flips heads with
probability 1/4.You randomly pick one of the coins and flip it
until you get a heads. Let X be the number of flips you need.
Compute E[X] and Var[X]
A biased coin has probability p = 3/7 of flipping heads. In a
certain game, one flips this coin repeatedly until flipping a total
of four heads.
(a) What is the probability a player finishes in no more than 10
flips?
(b) If five players independently play this game, what is the
probability that exactly two of them finish in no more than ten
flips?
You are given an unfair coin (the probability of heads is 1/3)
and decide to toss it ten times. Following Example 5.3 in your
textbook, plot the binomial probability mas function for N = 10 and
p = 1/3. What is the probability that the coin will come up heads 5
times in 10 tosses?
Determine the mean, variance, and joint second moments.
a. Y = cos
You are tossing a coin and it has a probability of p to show
heads on any given toss. You keep on tossing the coin until you see
a heads. Let X represent the number of tosses until you see a
heads.
1. Find the probability that X is odd.
2. Find the probability that X is even, DO NOT USE QUESTION
1.
3. Let's say the coin is balanced, what is the probability that X
is odd? Is this...
Analysis question
The probability of landing heads in a coin toss is 1/2. Use
this information to explain why the remaining number of pennies is
reduced by about half each time they are shaken and tossed.
Section I
You toss a coin and roll a die simultaneously. If the coin shows
heads, the experiment outcome is equal to the value shown on the
die. If the coin shows tails, the experiment outcome is equal to
twice the value shown on the die. Assume that the coin and the die
are fair. Let ? be 1 if the coin shows heads and 2 if the coin
shows tails, ?be the outcome of rolling the die, and ?...
1. Amy tosses 12 biased coins. Each coin comes up heads with
probability 0.2. What is the probability that fewer than 3 of the
coins come up heads?
Answer: 0.5583
2. Amy shoots 27000 arrows at a target. Each arrow hits the
target (independently) with probability 0.2. What is the
probability that at most 2 of the first 15 arrows hit the
target?
Answer: 0.398
3. Amy tosses 19 biased coins. Each coin comes up heads with
probability 0.1. What...
1.
a)If you were to toss a coin twice. What is the probability that
it would come up Heads once and Tails once. Express you answer in
decimals to one place.
b)The sum of the probability of all outcomes
equals? Express your answer as a percentage to one
decimal place.