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The probability that at least two people in the group of 5 people will have the same birthday is:

1 - 365/365 x 364/365 x 363/365 x 362/365 x 361/365 = 0.027, which is

1 - (365 - 0)*(365 - 1)*(365 - 2)*(365 - 3)*(365 - 4) / 365^5 = 0.027

The probability that at least two people in the group of 10 people will have the same birthday is:

1 - 365/365 x 364/365 x 363/365 x 362/365 x 361/365 x 360/365 x 359/365 x 358/365 x 357/365 x 356/365 = 0.12, which is

1 - (365 - 0)*(365 - 1)*(365 - 2)*(365 - 3)*(365 - 4) )*(365 - 5)*(365 - 6)*(365 - 7)*(365 - 8)*(365 - 9)/ 365^10 = 0.12

So you can see that the probability is growing as the number of people in the group increases. We can say that for a group of 365 people the probability that at least two people will have the same birthday is 1.0 or 100%.

Using loops we need to create a program that will show the table: probability vs. number of people.

The table will display the minimum number of people that would be required so that the probability of at least two people in a randomly chosen group having the same birthday is at least 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1.0.

1 - 365/365 x 364/365 x 363/365 x 362/365 x 361/365 = 0.027, which is

1 - (365 - 0)*(365 - 1)*(365 - 2)*(365 - 3)*(365 - 4) / 365^5 = 0.027

The probability that at least two people in the group of 10 people will have the same birthday is:

1 - 365/365 x 364/365 x 363/365 x 362/365 x 361/365 x 360/365 x 359/365 x 358/365 x 357/365 x 356/365 = 0.12, which is

1 - (365 - 0)*(365 - 1)*(365 - 2)*(365 - 3)*(365 - 4) )*(365 - 5)*(365 - 6)*(365 - 7)*(365 - 8)*(365 - 9)/ 365^10 = 0.12

So you can see that the probability is growing as the number of people in the group increases. We can say that for a group of 365 people the probability that at least two people will have the same birthday is 1.0 or 100%.

Using loops we need to create a program that will show the table: probability vs. number of people.

The table will display the minimum number of people that would be required so that the probability of at least two people in a randomly chosen group having the same birthday is at least 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1.0.

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