Statistics

Probability

Top Answer

Given that this is discrete data and the probability of each outcome is the same, i.e. E(P(x=1))=0.5=E(P(x=0)), and the law of large numbers says that over many trials n the outcome of a value tends to its expectation, over 90 trials you would expect around 45 of the results to be heads. That is, n=90, E(x)=0.5, 90*0.5=45.

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030 maybe but i say 35 or 31

A fair coin would be expected to land on heads 10 times on average.

Roughly half of the time, so about 350 times.

A fair coin would be expected to land on heads 75 times.

The probability of a heads is 1/2. The expected value of independent events is the number of runs times the probability of the desired result. So: 100*(1/2) = 50 heads

This is a binomial probability distribution The probability of exactly 2 heads in 50 coin tosses of a fair coin is 1.08801856E-12. If you want to solve this for how many times 50 coin tosses it would take to equal 1 time for it to occur, take the reciprocal, which yields you would have to make 9.191019648E11 tosses of 50 times to get exactly 2 heads (this number is 919,101,964,800 or 919 billion times). If you assume 5 min for 50 tosses and 24 hr/day tossing the coin, it would take 8,743,360 years. That is the statistical analysis. As an engineer, looking at the above analysis, I would say it is almost impossible flipping the coin 50 times to get exactly 2 heads or I would not expect 2 heads on 50 coin tosses. So, to answer your question specifically, I would say none.

This is a binomial probability distribution The probability of exactly 2 heads in 50 coin tosses of a fair coin is 1.08801856E-12. If you want to solve this for how many times 50 coin tosses it would take to equal 1 time for it to occur, take the reciprocal, which yields you would have to make 9.191019648E11 tosses of 50 times to get exactly 2 heads (this number is 919,101,964,800 or 919 billion times). If you assume 5 min for 50 tosses and 24 hr/day tossing the coin, it would take 8,743,360 years. That is the statistical analysis. As an engineer, looking at the above analysis, I would say it is almost impossible flipping the coin 50 times to get exactly 2 heads or I would not expect 2 heads on 50 coin tosses. So, to answer your question specifically, I would say none.

Expected number of heads is 1/4 * 32 or 8 heads.

the probability of getting heads-heads-heads if you toss a coin three times is 1 out of 9.

yes the coin is biased because it turned to heads 36 times.

A fair coin means that the probability of a head = probability of a tail = 1/2 So you would expect half the tosses to be heads, ie 1/2 x 75 = 371/2 heads. ...oooOOOooo... Having 1/2 a head doesn't seem possible, but when the question asks about expectation, it is saying: if you repeated the experiment lots of times, how often, on average, would the required result appear. So the expectation of heads when a fair coin is tossed 75 times is asking: if a fair coin was repeatedly tossed 75 times, what would be the (mean) average number of heads achieved? As more and more trials are done and the (mean) average of the number of heads got is taken, it will get closer and closer to 371/2 37 or 38 times. (Obviously, you can't have half of a time.) You will either get one or the other, and a fair coin means that either is just as likely. So, it should split evenly down the middle.

If you toss a coin 10 times and count 58 heads, you know the coin is NOT fair.

None, since that would imply that in 18 cases the coin did not show heads or tails!

Since it is a fair coin, the probability is 0.5

The answer depends on "the outcome is heads HOW MANY TIMES!"

The probability of flipping a coin 3 times and getting 3 heads is 1/2

The correct answer is 1/2. The first two flips do not affect the likelihood that the third flip will be heads (that is, the coin has no "memory" of the previous flips). If you flipped it 100 times and it came up heads each time, the probability of heads on the 101st try would still be 1/2. (Although, if you flipped it 100 times and it came up heads all 100 times - the odds of which are 2^100, or roughly 1 in 1,267,650,000,000,000,000,000,000,000,000 - you should begin to wonder about whether it's a fair coin!). If you were instead asking "What is the probability of flipping a coin three times and having it land on "heads" all three times, then the answer is 1/8.

Less. The more times the coin is tossed, the more likely it will reflect the actual odds of .5 heads and .5 tails.

HeadsTailsTailsTailsHeadsTailsHeads

Possibly not - the sample of 60 times is very small.

The probability that the coin will land on heads each time is 1/2. (1/2) to the tenth power is 1/1024. This is the probability that the coin will not land on heads. Subtract it from one to get the probability that it will : 1-(1/1024)There is a 1023/1024 or about 99.90234% chance that the coin will land on heads at least once.(There is a 1/1024 chance that the coin will land on heads all four times.)

the probability is actually not quite even. It would actually land heads 495 out of 1000 times because the heads side is slightly heavier

The probability of flipping a coin 24 times and getting all heads is less than 1 in 16 million. (.524) It would seem that no one has ever done that.

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