Math and Arithmetic

Statistics

Probability

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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

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0A fair coin would be expected to land on heads 10 times on average.

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

It means that if the coin were tossed an infinite number of times, half of the tosses would come up heads and half would be tails.

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

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.

Roughly half of the time, so about 350 times.

The expected number is 3750.

If you look at this in a "fair way," it would be 1/8. However, realistically, it has been proven that the heads side weighs slightly more that the tails side so that percentage (12.5%) would decrease.

Since each coin would have the outcome with Heads and Tails: Then among the 32 coins, we can have the possible outcomes from no Heads, 1 Head, 2 Heads, ....... , 31 Heads, 32 Heads. Therefore we would have 33 outcomes.

Each coin has 2 outcomes. Either being heads or tails. Take the outcome of each coin to the root of the number of coins. (1/2)^3 = .125 = 12.5% or a 1 in 8 chance. Take .125 and times it by 100 to get the probability out off 100 times. .125 x 100 = .125 which = 12.5%= 1 in 8 chance

The theoretical probability of HT or TH when two coins are tossed is 1/2 . (All possible outcomes are HH,TT,HT,TH). This means that when we run the experiment repeatedly we expect to get the desired result 1/2 of the time. Since you intend to toss the coins 40 times, 20 are expected.

25. In one throw the odds are 2/8. That is, th ere are 8 possible outcomes, two of which are considered "winning" combinations (HHH and TTT). In 100 throws, you would expect each of the 8 outcomes to occur 12 or 13 times (the average of the number of times each of the 8 outcomes occurs will always be exactly 12.5, whether the distribution is even or whether you got all heads all 100 throws and all the other combinations were zero). You would expect the number of times you get all heads or all tails - two of those combinations - to be 25.

You can expect to get a 5 about 15 times out of 90.

With a fair die, you would expect it 60*(1/6) = 10 times.

He should expect it 100 times.

You would expect it 0.3 of the times.

You can expect the spinner to land an odd number 25 times out of 50.

Every time you flip a coin it has a 50% probability that it will land on either heads or tails. You would expect to get heads about half the time and tails about half the time. What actually happens could be different from what is expected. You could get heads every time, or tails every time. Or you could get tails 75% of the time and heads 25% of the time. however, your results appear to be what you would expect, approximately 50% heads and 50% tails. You got 16 heads and 14 tails. Your percentage of heads is 16/30 x 100= 53.33... %. Your percentage of tails is 14/30 x 100 = 46.66... %.

9, you just have to multiply for problems like this

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

1/6 of 300 = 50 times.

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.

I would expect it to land on a number of 4 or higher 50% of the time or roughly 24 times.

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