Question

A biased coin is tossed ten times. Given that exactly four Heads were obtained, what is the conditional probability that exactly two Heads were obtained in the first five tosses?

Answer #1

We use Bayes rule to calculate this one. The detailed explanation is given in the picture attached.

we assume here p,q are not equal to zero.

A fair coin is tossed 4 times.
What is the probability of getting exactly 3 heads conditioned
on the event that the first two tosses came out the same?

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..?

A coin is tossed 7 times. What is the probability that the
number of heads obtained will be 6? Express your answer as a
fraction or a decimal number rounded to four decimal places.

A coin is tossed 100 times and the results are recorded. 40
times the coin lands on heads, the other 60 times the coin lands on
tails. If 40 of the recorded tosses were selected at random, what
is the probability that the coin landed on heads exactly 14
times?

A fair coin is tossed for n times independently. (i) Suppose
that n = 3. Given the appearance of successive heads, what is the
conditional probability that successive tails never appear? (ii)
Let X denote the probability that successive heads never appear.
Find an explicit formula for X. (iii) Let Y denote the conditional
probability that successive heads appear, given no successive heads
are observed in the first n − 1 tosses. What is the limit of Y as n...

A coin is tossed 6 times. What is the
probability that the number of heads obtained will be between
2 and 3 inclusive? Express your answer as a
fraction or a decimal number rounded to four decimal places.
PLEASE DON'T ANSWER UNLESS YOU ARE CONFIDENT YOU KNOW
THE SOLUTION.

NOTE:KINDLY SOLVE PARTS D AND E.
A fair coin is tossed four times, and the random variable X is
the number of heads in the first three tosses and the random
variable Y is the number of heads in the last three tosses.
a) What is the joint probability mass function of X and Y ?
b) What are the marginal probability mass functions of X and Y
?
c) Are the random variables X and Y independent?
d) What...

A coin is tossed 5 times. Find the probability that exactly 2
are heads.
The probability that exactly 2 are heads is?
(Type an integer or decimal rounded to the nearest thousandth
as needed.)

A fair coin is tossed three times. Let X be the number of heads
among the first two tosses and Y be the number of heads among the
last two tosses. What is the joint probability mass function of X
and Y? What are the marginal probability mass function of X and Y
i.e. p_X (x)and p_Y (y)? Find E(X) and E(Y). What is Cov(X,Y) What
is Corr (X,Y) Are X and Y independent? Explain. Find the
conditional probability mass...

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)

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