Question

Suppose you toss an unfair coin 8 times independently. The probability of getting heads is 0.3. Denote the outcome to be 1 if you get heads and 0 if you get tails.

1.Write down the sample space.

2. What is the probability of the event that you get a head or a tail at least once?

3. If you get 8 same toss you will get x dollars, otherwise you will lose one dollar. On average, how large should x be to guarantee that you will not lose money in the long run?

(3)
8 of the samw tosess

Answer #1

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)...

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?

Determine the probability of getting a tail of a unfair coin
given that this coin on average, in 1.5 out of 100 attempts, takes
3 or more flips to get its first Head. For example, TTTH or TTTTTTH
happens 1.5 times on average out of 100 attempt.

A fair coin is tossed three times. What is the probability
that:
a. We get at least 1 tail
b. The second toss is a tail
c. We get no tails.
d. We get exactly one head.
e. You get more tails than heads.

An unfair coin is made so that heads is seven times as likely to
come up as tails when the coin is flipped. An experiment consists
of flipping this coin just once
What weight (or probability) does the outcome 'heads'
have?
What weight (or probability) does the outcome 'tails' have?
Enter your answers as whole numbers or fractions in lowest
terms.
An experiment has sample space S={a,b,c,d,e}. Outcomes b,c,d,e
are equally likely while the likelihood of outcome a is
Wa=7/19...

Suppose that an unfair coin comes up heads 52.2% of the time.
The coin is flipped a total of 19 times.
a) What is the probability that you get exactly 9 tails?
b) What is the probability that you get at most 17 heads?

You toss a fair coin four times. The probability of two heads
and two tails is

a) Suppose we toss a fair coin 20 times. What is the probability
of getting between 9 and 11 heads?
b) Suppose we toss a fair coin 200 times. What is the
probability of getting between 90 and 110 heads?

A certain “unfair” coin is one where the probability of a head
showing when flipped is 0.35 and the probability of a tail showing
is 0.65. An experiment consists of flipping 8 of these “unfair”
coins. Let the random variable x be the number of tails showing.
Determine the probability of 3 of the 8 coins showing tails.

A weighted coin has a probability of 0.6 of getting a head and
0.4 of getting a tail.
(a) In a series of 30 independent tosses what is the probability
of getting the same number of heads as tails? [2]
(b) Find the probability of getting more than 7 heads in 10
tosses? [3]
(c) Find the probability of 4 consecutive tails followed by 2
tails in the next 6 tosses. [2]

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