Find the probability of getting 8 heads in 12 tosses of a coin.

Solutions

Expert Solution

when a coin is flipped, we get 2 outcomes = head or tail

If a coin is tossed 12 times, the maximum probability of getting heads is 12.
But, 12 coin tosses leads to number of possible sequences of heads & tails.

The number of possible sequences of heads and tails in 12 coin tosses is:

The number of ways that such a sequence could contain 8 heads is the number of ways of choosing 8 out of 12

that is

nCr = n! / r! * (n - r)!,

12C8 =

So the probability of getting 8 heads in 12 coin tosses is

orchestra answered 1 year ago

Next > < Previous

Related Solutions

(a) Find the exact probability of exactly 55 heads in 100 tosses of a coin. (b)...

(a) Find the exact probability of exactly 55 heads in 100 tosses of a coin. (b) Estimate this probability using normal distribution. Compare your answers.

1. Amy tosses 12 biased coins. Each coin comes up heads with probability 0.2. What is...

1. Amy tosses 12 biased coins. Each coin comes up heads with probability 0.2. What is the probability that fewer than 3 of the coins come up heads? Answer: 0.5583 2. Amy shoots 27000 arrows at a target. Each arrow hits the target (independently) with probability 0.2. What is the probability that at most 2 of the first 15 arrows hit the target? Answer: 0.398 3. Amy tosses 19 biased coins. Each coin comes up heads with probability 0.1. What...

a) A coin is flipped 6 times, find the probability of getting exactly 4 heads. Hint: The Binomial...

a) A coin is flipped 6 times, find the probability of getting exactly 4 heads. Hint: The Binomial Distribution Table can be very helpful on questions 19-21. If you use the table for this question, give your answer exactly as it appears. If you calculated your answer, round to the thousandths place. b) A coin is flipped 6 times. Find the probability of getting at least 3 heads. If you used a table to help find your answer, give it to the thousandths place....

In 10,000 tosses of a coin, 5080 heads occurred. Find a 95% confidence interval for the...

In 10,000 tosses of a coin, 5080 heads occurred. Find a 95% confidence interval for the true proportion of heads, and then decide (based upon that confidence interval) whether the coin is fair or not.

A coin is tossed thrice. Find the probability of getting

A coin is tossed thrice. Find the probability of getting (i) exactly two heads. (ii) at least two tails.

sean tosses a coin 40 times and gets 15 heads while Micah tosses a coin 30...

sean tosses a coin 40 times and gets 15 heads while Micah tosses a coin 30 times and gets 16 heads. Suppose that the outcomes of sean's coin tosses are iid random variable with probability p1 of getting heads on each toss while Micah’s outcomes are also iid with a potentially different probability p2 of getting heads. (1) Calculate the maximum likelihood and method of moments estimators of p1. (2) Show that the MLE of p1 is an MVUE for...

A coin is flipped seven times. What is the probability of getting heads six or fewer...

A coin is flipped seven times. What is the probability of getting heads six or fewer times? I know how to solve this with the probability equation. 2x2x2x2x2x2x2=128 total outcomes Which is p1+p2=1 -> p1=1-p2-=1-1/128= 127/128 is the answer. But whenever I try to solve it with the permutation formula I get a wrong answer n!/ k!(n!-k!) = 7!/6!(7!-6!) = 7 7/128 where am I wrong? can someone explain to me what am I doing wrong?

What’s the probability of flipping a coin 25 times and getting between 32% and 50% heads....

What’s the probability of flipping a coin 25 times and getting between 32% and 50% heads. Please assume that this clearly discrete distribution is, in fact, continuous, and use the normal approximation.

What’s the probability of getting no heads after flipping a fair coin 10 times? What’s the...

What’s the probability of getting no heads after flipping a fair coin 10 times? What’s the probability of getting no 3’s after rolling a fair 6-sided die 9 times? What’s the probability of getting a 4 at least once after rolling a fair 4-sided die 5 times? What’s the probability of getting a 5 exactly once after rolling a fair 8-sided die 7 times?

Fair Coin? In a series of 100 tosses of a token, the proportion of heads was...

Fair Coin? In a series of 100 tosses of a token, the proportion of heads was found to be 0.43. However, the margin of error for the estimate on the proportion of heads in all tosses was too big. Suppose you want an estimate that is in error by no more than 0.05 at the 90% confidence level. (a) What is the minimum number of tosses required to obtain this type of accuracy? Use the prior sample proportion in your...

Subjects