Math and Arithmetic
Statistics
Probability

# Suppose you toss a fair coin 75 times how many times would you expect to get heads?

###### Answered 2012-06-04 04:32:17

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.

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## Related Questions

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.

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.

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

It would be 50% of the time. The question gives a time line of from his 12th birthday to his 18th birthday but that information wasn't needed. The question is basically you have a coin... you flip it. what is the odds that it lands on heads so Kalvin enjoys a bowl of his favorite Cocoa Blast Cereal. This is wrong because it is asking your for a prediction of how many times he would eat the cereal not the chance that the coin has to be heads. Answer is 50 % of the time.

You would expect rain, the idea being because weather tends to move from west to east in this country due to the Westerlies.

I suppose it would be too much to expect you to say how much the tiles cost!

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

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.

Working with colleagues can be a challenge at times. One would expect, trust, and mutual respect for one another in the workplace.

How do you suppose we are going to do this.I suppose that would be easy to do.

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