Analysis question The probability of landing heads in a coin toss is 1/2. Use this information...

Analysis question

The probability of landing heads in a coin toss is 1/2. Use this information to explain why the remaining number of pennies is reduced by about half each time they are shaken and tossed.

Expert Solution

We are given that the probability of landing heads in a coin toss is ½. If the coin is fair, then the probability of getting head or tail is equal to ½. If all coins or pennies are fair, then the probability of landing heads will be ½ or approximately equal ½. Although we will not get exactly half of the heads from all coins flipped at the same time, but if we repeated the experiment several times, then the expected value for getting head becomes ½. So, according to sampling distribution rule, the proportion of getting head will approach probability ½ as we increase the number of trials.

orchestra answered 2 years ago

Ken has a coin that has probability 1/5 of landing Heads. Mary has a coin that...

Ken has a coin that has probability 1/5 of landing Heads. Mary has a coin that has probability 1/3 of landing Heads. They toss their coins simultaneously, repeatedly. Let X be the number of tosses until Ken gets his first Heads. Let Y be the number of tosses until Mary gets her first Heads. Find: Let U = min(X,Y) and V = max(X,Y) (d) For k = 1, 2, 3,... , find a formula for P(U = k). (e) For...

Use MATLAB to plot the likelihood function for estimating the probability of a coin landing heads-up...

Use MATLAB to plot the likelihood function for estimating the probability of a coin landing heads-up without prior knowledge after observing HTHT. -would greatly appreciate if you went in detail on how to find the likelihood function based off the given information.

You toss a biased coin with the probability of heads as p. (a) What is the...

You toss a biased coin with the probability of heads as p. (a) What is the expected number of tosses required until you obtain two consecutive heads ? (b) Compute the value in part (a) for p = 1/2 and p = 1/4.

You are given an unfair coin (the probability of heads is 1/3) and decide to toss...

You are given an unfair coin (the probability of heads is 1/3) and decide to toss it ten times. Following Example 5.3 in your textbook, plot the binomial probability mas function for N = 10 and p = 1/3. What is the probability that the coin will come up heads 5 times in 10 tosses? Determine the mean, variance, and joint second moments. a. Y = cos

Coin 1 comes up heads with probability 0.6 and coin 2 with probability 0.5. A coin...

Coin 1 comes up heads with probability 0.6 and coin 2 with probability 0.5. A coin is continually ﬂipped until it comes up tails, at which time that coin is put aside and we start ﬂipping the other one. (a) What proportion of ﬂips use coin 1? (b) If we start the process with coin 1 what is the probability that coin 2 is used on the ﬁfth ﬂip? (c) What proportion of ﬂips land heads?

(A) Discuss the probability of landing on heads if you flipped a coin 10 times? (B)...

(A) Discuss the probability of landing on heads if you flipped a coin 10 times? (B) What is the probability the coin will land on heads on each of the 10 coin flips? (C) Apply this same binomial experiment to a different real-world situation. Describe a situation involving probability? please explain each and show work. showing the steps to the answer would be great..

Suppose that coin 1 has probability 0.8 of coming up heads, and coin 2 has probability...

Suppose that coin 1 has probability 0.8 of coming up heads, and coin 2 has probability 0.6 of coming up heads. If the coin flipped today comes up heads, then with equal probability we select coin 1 or coin 2 to flip tomorrow, and if it comes up tails, then we select coin 2 to flip tomorrow. (a) If the coin initially flipped is coin 1, what is the probability that the coin flipped on the second day after the...

A coin is tossed 400 times, landing heads up 219 times. Is the coin fair?

Section I You toss a coin and roll a die simultaneously. If the coin shows heads,...

Section I You toss a coin and roll a die simultaneously. If the coin shows heads, the experiment outcome is equal to the value shown on the die. If the coin shows tails, the experiment outcome is equal to twice the value shown on the die. Assume that the coin and the die are fair. Let ? be 1 if the coin shows heads and 2 if the coin shows tails, ?be the outcome of rolling the die, and ?...

6. Create a probability distribution for a coin flipping game. That is, toss a coin at...

6. Create a probability distribution for a coin flipping game. That is, toss a coin at least 25 times and keep up with the number of heads and the number of tails. (8 points for each part) a. Compile your data into a probability distribution. Be sure to show that your distribution meets the properties for a probability distribution. RESULTS Trial 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19...

Question