Question

4. The Casino Control Commission takes a coin from a casino it suspects to be unfair. They flip the coin 10 times and lands on heads 8 times.

(a) What is the probability that a fair coin would land on heads at least 8 times?

(b) Based on your answer to the last question, do you think the coin is unfair? Explain.

5. Every day, Janet either takes the bus or drives her car to work. She drives her car 30% of the time. When she drives her car, she packs her lunch 70% of the time. When she takes the bus she packs her lunch 20% of the time.

(a) Given that Janet rode the bus, what is the probability that she did not pack her lunch?

(b) Given that Janet did not pack her lunch, what is the probability that she rode the bus?

6. One fair coin and two unfair coins where heads is 5 times as likely as tails are put into a bag. One coin is drawn at random and then flipped twice. If at least one of the flips was tails, what is the probability an unfair coin was flipped?

Answer #1

We would be looking at Q4 here:

The number of heads in 10 tosses is modelled here as:

a) The probability of getting at least 8 heads is computed here as:

**Therefore 0.0546875 is the required probability
here.**

b) As the probability is 0.0546875 > 0.05, therefore the
event is not unusual here. **Therefore we dont have evidence
here that the event is unusual.**

One fair coin and two unfair coins where heads is 5 times as
likely as tails are put into a bag. One coin is drawn at random and
then flipped twice. If at least one of the flips was tails, what is
the probability an unfair coin was flipped?
Every day, Janet either takes the bus or drives her car to work.
She drives her car 30% of the time. When she drives her car, she
packs her lunch 70%...

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?

An unfair coin is flipped 3 times, heads is 4 times as likely to
occur than tails.
x= the number of heads.
Find the probability distribution, E(x), and σ(x).

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...

4. A fair coin is flipped 6 times.
a. what is the distribution
of outcomes?
b. what is the probability
of getting 4 heads/2 two tails in six flips of a
coin?

Slim and Roy are flipping a unfair coin, where the coin has the
chance to land on heads 65% of the time. Every time that the coin
lands on heads, Slim gets 500 dollars from Roy, and Roy gets 500
dollars from Slim if the coin lands on tails. If the game is played
100 times (coin is flipped 100 times), what is the probability that
Slim's winnings are $20,000 more than Roy's, where 'x' is strictly
greater than 20,000...

A coin is weighted so that there is a 63% chance that it will
come up "heads" when flipped.
The coin is flipped four times. Find the probability of at least
one of the flips resulting in "tails".
Round your answer to four decimal places.

Suppose Tori has an unfair coin which lands on Tails with
probability 0.28 when flipped. If she flips the coin 10 times, find
each of the following:
The mean number of Tails
P(Less than or equal to 2 Tails)
P(No more than 3 Tails)
P(No Tails)
P(At least 1 Tail)
P(Exactly 1 Tail)
P(Exactly 4 Tails)
P(At least 5 Tails)
P(More than 3 Tails)
The standard deviation of the number of Tails
1.
0.1798
2.
0.7021
3.
2.8
4.
0.1181...

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...

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?

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