Question

4. (5pts) You have three coins A, B, andC. The coin A is fair.
The probability that a head willshowwhenB istossedis 2 3,whileitis
1 3 inthecaseofthecoinC. Acoinischosenat random and tossed 3 times
giving 2 heads and 1 tail. Find the probability that the coin A
waschosen.

Could you provide me the detailed process of this question. And what formula you are using for?

Answer #1

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.

You select a coin at random: 2/3 of the coins are unfair, 1/3 of
the coins are fair. The fair coins are equally likely to flip heads
or tails. The unfair coins flip heads 3/4 of the times, and tails
1/4 of the times. You flip the selected coin and get heads or
tails. Find (1) the probability that the selected coin is fair
given the flip is heads, (2) the probability that the selected coin
is fair given the...

suppose a box contains three coins. two are fair and one is a
coin with two tails. a coin is randomly selected from the box and
tossed once.
a) what is the probability that the result of the toss is a
tail?
b) Given the result of the toss is a tail, what is the
probability that the selected coin is the one with two tail?

Coin 1 and Coin 2 are biased coins. The probability that tossing
Coin 1 results in head is 0.3. The probability that tossing Coin 2
results in head is 0.9. Coin 1 and Coin 2 are tossed
(i) What is the probability that the result of Coin 1 is tail
and the result of Coin 2 is head?
(ii) What is the probability that at least one of the results is
head?
(iii) What is the probability that exactly one...

There are X, Y and Z coins in a box. X is a fair coin; Y is a
coin with tail on both sides and Z is a coin with a probability of
2/5 of the head. Let's imagine we pulled a random coin out of the
box. Since it is known that it is tail, what is the probability
that this money will be X?
A. 1/3
B. 7/10
C. 5/21
D. 3/5

A magician has 20 coins in his pocket. Twelve of these coins are
normal fair coins (with one head and one tail) and eight are
defective coins with heads on both sides. The magician randomly
draws a coin from his pocket and flips it. Given that the flipped
coin shows a head, what is the probability that it is
defective?
Select one:
4/7
8/20
1
1/2

suppose you took a fair coin tossed it five times , if you obtained
five heads, is it more likely that the next toss will be a head or
tail ? explain

Consider an experiment of tossing two coins three times. Coin A
is fair but coin B is not with P(H)= 1/4 and P(T)= 3/4. Consider a
bivariate random variable (X,Y) where X denotes the number of heads
resulting from coin A and Y denotes the number of heads resulting
from coin B.
(a) Find the range of (X,Y)
(b) Find the joint probability mass function of (X,Y).
(c) Find P(X=Y), P(X>Y), P(X+Y<=4).
(d) Find the marginal distributions of X and...

Given a fair coin, if the coin is flipped n times, what is the
probability that heads is only tossed on odd numbered tosses.
(tails could also be tossed on odd numbered tosses)

A black bag contains two coins: one fair, and the other biased
(with probability 3/4 of landing heads). Suppose you pick a coin
from the bag — you are twice as likely to pick the fair coin as the
biased one — and flip it 8 times. Given that three of the first
four flips land heads, what is the expected number of heads in the
8 flips?

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