Question

Find the probability of each of the following events:

(i) Tossing a coin 5 times with the outcome of five heads.

(ii) Tossing four coins with the outcome of two heads and two tails in any order.

Answer #1

A biased coin is flipped 9 times. If the probability is 14 that
it will land on heads on any toss. Calculate: This is a binomial
probability question
i) The probability that it will land heads at least 4
times.
ii) The probability that it will land tails at most 2 times.
iii) The probability that it will land on heads exactly 5
times.

Using R, simulate tossing 4 coins as above, and compute the
random variable X(the outcome of tossing a fair coin 4 times &
X = num of heads - num of tails.). Estimate the probability mass
function you computed by simulating 1000 times and averaging.

A coin is tossed five times. By counting the elements in the
following events, determine the probability of each event. (Show
your work)
a. Heads never occurs twice in a row.
b. Neither heads or tails occur twice in a row
c. Both heads and tails occur at least twice in a row.
The answers are 13/32, 1/16, and 1/4. I'm just stuck on how to
get them.

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 coin is tossed seven times. What is the probability that the
outcome is seven heads, given that exactly four of the coins show
heads?
The probability of getting seven heads is..?

When coin 1 is flipped, it lands on heads with probability
3
5
; when coin 2 is flipped it lands on heads with probability
4
5
.
(a)
If coin 1 is flipped 11 times, find the probability that it
lands on heads at least 9 times.
(b)
If one of the coins is randomly selected and flipped 10 times,
what is the probability that it lands on heads exactly 7
times?
(c)
In part (b), given that the...

1.
two coins are tossed, find the probability that two heads are
obtained. note: each coin has two possible outcomes H (heads) and T
(tails).
2. which of these numbers cannot be a probability? why?
a) -0.00001
b) 0.5
c) 20%
d)0
e) 1
3. in a deck of 52 cards, what is the probability of drawing a
three of spades, and then a four of clubs, without
replacement?
4. what is the probability of the same outcome in #3,...

(Q6) A coin is biased so that the probability of tossing a head
is 0.45. If this coin is tossed 55 times, determine the
probabilities of the following events. (Round your answers to four
decimal places.)
(a) The coin lands heads more than 21 times.
(b) The coin lands heads fewer than 28 times.
(c) The coin lands heads at least 20 times but at most 27
times.
(Q7) A company finds that one out of three employees will be...

An experiment consists of tossing a coin 6 times. Let X
be the random variable that is the number of heads in the outcome.
Find the mean and variance of X.

Suppose my friend and I are tossing a biased coin (the chance of
the coin landing heads is p> 1/2). I get one dollar each time
the coin lands heads, and I have to pay one dollar to my friend
each time it lands tails. I will stop playing if my net gain is
three dollars (net gain = amount won-amount lost).
a) What is the chance that i will stop after exactly three
tosses?
b) What is the chance...

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