Question

Consider the biased coin that produces head 70% of the time from the probability calculation in...

Consider the biased coin that produces head 70% of the time from the probability calculation in week 2. One tosses the coin twice. Conditioning on that we know both tosses have the same outcome, what is the probability of that both tosses are tails?

1- 0.09

2- 0.125

3- 0.155

4- 0.5

Homework Answers

Answer #1

We’re told (a) that the coin is biased 70% heads and 30% tails and (b) that both tosses have the same outcome: i.e. they are both heads or both tails.

Assuming the tosses are independent of one another, the probability of getting two heads is (.7)*(.7)=0.49.

The probability of getting two tails is

(.3)*(.3)=0.09.

As the question says, the total probability of getting two of the same outcome is the sum of these or 0.49+0.09=0.58.

since the two outcomes being studied are mutually exclusive of these ,

0.49/0.58=0.844

And are two heads and

0.09/0.58=0.1552 is two tailes.

Therefore, answer is

3)0.155

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Consider a biased coin with the probability of getting a Head 0.59 and the probability of...
Consider a biased coin with the probability of getting a Head 0.59 and the probability of getting a Tail 0.41. You keep tossing this coin until you get both a Head as well as a Tail. Let X be the number of tosses required. Compute E(X).
A weighted coin has a probability of 0.6 of getting a head and 0.4 of getting...
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]
Suppose we toss a biased coin independently until a random time N independent of the outcomes...
Suppose we toss a biased coin independently until a random time N independent of the outcomes of the tosses. Where N takes values 1,2,3 with probability 0.3, 0.5, 0.2. Find E(X1 + ··· XN) where Xi = 1 if head-on i th toss with probability 0.55 and zero otherwise, (for i = 1, ··· , N).
Problem 1. Consider independent tosses of the same coin. The probability that the coin will land...
Problem 1. Consider independent tosses of the same coin. The probability that the coin will land on head is p and tails is 1-p. HHTTTTHHTHHHHHHHHTTHHHHHH a. What is the probability of this specific series of tosses (also known as the likelihood of the data)? Assume each toss is independent. (2 pts) b. Is the likelihood greater for p = .6 or p = .7? (1 pt) c. What value of p maximizes the likelihood for n tosses of which k...
A particular coin is biased. Each timr it is flipped, the probability of a head is...
A particular coin is biased. Each timr it is flipped, the probability of a head is P(H)=0.55 and the probability of a tail is P(T)=0.45. Each flip os independent of the other flips. The coin is flipped twice. Let X be the total number of times the coin shows a head out of two flips. So the possible values of X are x=0,1, or 2. a. Compute P(X=0), P(X=1), P(X=2). b. What is the probability that X>=1? c. Compute the...
URGENT!!! PLEASE ANSWER QUICKLY!! Consider 68 independent tosses of a coin with probability of a head...
URGENT!!! PLEASE ANSWER QUICKLY!! Consider 68 independent tosses of a coin with probability of a head equal to 0.7. Let X and Y be the numbers of heads and of tails, respectively. Compute the covariance of X and Y . Round your answer to four decimal digits after the decimal point.
Deriving fair coin flips from biased coins: From coins with uneven heads/tails probabilities construct an experiment...
Deriving fair coin flips from biased coins: From coins with uneven heads/tails probabilities construct an experiment for which there are two disjoint events, with equal probabilities, that we call "heads" and "tails". a. given c1 and c2, where c1 lands heads up with probability 2/3 and c2 lands heads up with probability 1/4, construct a "fair coin flip" experiment. b. given one coin with unknown probability p of landing heads up, where 0 < p < 1, construct a "fair...
(Q6) A coin is biased so that the probability of tossing a head is 0.45. If...
(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...
1) Let S = {H, T} be the sample space associated to the fair coin-flipping. Is...
1) Let S = {H, T} be the sample space associated to the fair coin-flipping. Is {H} independent from {T}? 2) Let S = {HH, HT, TH, T T} be the sample space associated to flipping fair coin twice. Consider two events A = {HH, HT} and B = {HT, T H}. Are they independent? 3) Suppose now we have a biased coin that will give us head with probability 2/3 and tail with probability 1/3. Let S = {HH,...
A biased coin (one that is not evenly balanced) is tossed 6 times. The probability of...
A biased coin (one that is not evenly balanced) is tossed 6 times. The probability of Heads on any toss is 0.3. Let X denote the number of Heads that come up. 1. Does this experiment meet the requirements to be considered a Bernoulli Trial? Explain why or why not. 2. If we call Heads a success, what would be the parameters of the binomial distribution of X? (Translation: find the values of n and p) 3. What is the...
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT