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The probability that a coin turns up heads when it is tossed is 1/2. Does that mean if...

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xetaalpha2 | Student | Honors

Posted January 19, 2011 at 10:59 AM via web

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The probability that a coin turns up heads when it is tossed is 1/2. Does that mean if the coin is tossed twice, we will get one heads?

 

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kjcdb8er | Teacher | (Level 1) Associate Educator

Posted January 19, 2011 at 11:16 AM (Answer #1)

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The probability is 1/2 because there are only two outcomes: heads or tails. Since it is equally likely that either a heads or a tails will result from a coin flip, this means that the probability of either event is 50%.

You can compare probability to an average. Just because the average grade in a class is 80% doesn't mean that if you pick two people in the class both will have a grade of 80%.

You know from experience that if  you flip a coin twice, sometimes you get tails twice in a row. That is because each time you flip the coin, the odds remain 1/2; the two flips are independent of each other. The odds of getting tails twice in a row are 1/2 * 1/2 = 1/4. So 25% of the time you'll get heads twice in a row.

The odds of flipping a coin 100 times, and getting 100 heads is 1/2^100 = 1/1.2676506 × 1030

But, if you've already flipped a coin 99 times, and gotten heads each time, then the odds of your next flip being heads is still just 50:50.

However, if you have actually flipped a coin 100 times, probably you will have gotten heads about 50 times and tails about 50 times, because this is the most likely average outcome. But, it doesn't have to be like that.

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justaguide | College Teacher | (Level 2) Distinguished Educator

Posted January 19, 2011 at 11:04 AM (Answer #2)

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The probability that the coin when tossed turns up heads is 1/2. This means that when the coin is tossed, the probability of tails is 1 – 1/2 = 1/2.

When the coin is tossed twice, the probability of getting only tails is 1/2* 1/2 = 1/4. The probability of getting at least one heads is 1 – 1/4 = 3/4.

Now, we have to remember that the probability of getting a heads equal to 1/2 does not mean that for every two tosses, one is definitely going to be heads and the other tails. Though if we continue to toss the coin a very large number of times, we will find that the number of times it turns up tails is very close to the number of times it turns up heads.

So if you do not get a tails the first time you shouldn’t bet all your money on tails the next time as the probability of your losing all your money remains the same, 1/2.

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hala718 | High School Teacher | (Level 1) Educator Emeritus

Posted January 19, 2011 at 11:06 AM (Answer #3)

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No it does not mean that we will get head.

This is called an "independent event".

The probability of the first toss does not affect the second toss.

So, when we calculate the probability we multiply each toss.

For example.

Probability of getting head the first toss = 1/2

The probability of getting head the second toss  = 1/2

The probability of getting head first and second = 1/2 * 1/2 = 1/4

So the difference is we multiply the probabilities in the independent events.

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