# Heads occurs 15 times out of 20 - Is it a fair coin?

• phono
In summary, the conversation discusses the task of proving that 96% of the time, the number of heads in 20 flips will be between 6 and 14 inclusive. The use of expectation and probability is mentioned, as well as the consideration of standard deviation. The process of proving the 96% figure is explained, and the concept of a fair coin is also brought up.
phono

## Homework Statement

I have to answer this question by using references to expectation and probability as well as any other relevant considerations. My textbook says that 96% of the time, the number of heads in 20 flips will be between 6 and 14 inclusive. How do I prove this?

Do you know about the standard deviation?

phono said:
My textbook says that 96% of the time, the number of heads in 20 flips will be between 6 and 14 inclusive. How do I prove this?
Even if you answer this, it won't tell you the answer to the question in the thread title. Are you sure you gave us all the information?

Anyway, if you want to prove that 96% figure, you have to add up the probabilities for "exactly 6", "exactly 7" and so on. Do you know how to calculate those?

Heads occurs 15 times out of 20 - Is it a fair coin?

A fair coin is one which gives 50% heads and 50% tale when tossed for infinite number of times.

## 1. Is the coin biased?

No, based on the given information, there is a high likelihood that the coin is fair. Heads occurring 15 times out of 20 is within the expected range for a fair coin.

## 2. What is the probability of getting heads?

The probability of getting heads is 15/20 or 0.75. This means that there is a 75% chance of getting heads when flipping this coin.

## 3. How many times should I flip the coin to determine if it is fair?

To determine if the coin is fair, you should ideally flip it a large number of times, such as 100 or more. The more times you flip it, the more reliable your results will be.

## 4. Can this result occur by chance?

Yes, it is possible for this result to occur by chance. While the expected number of heads for a fair coin is 10 out of 20, there is always a possibility of getting slightly more or less heads due to random chance.

## 5. What other factors could affect the results of flipping a coin?

Other factors that could affect the results of flipping a coin include the weight distribution of the coin, the force used to flip it, and any external factors such as wind or surface texture. These factors can all contribute to the coin landing on one side more frequently than the other.

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