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Started 3 weeks ago by Bansita Swain in

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  • Replied 11 months ago

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    Hi Banista, the probability of at least 2 people having the same birthday in a group of 12 people can be calculated using the complement rule.The complement rule states that the probability of an event not happening is equal to 1 minus the probability of the event happening.In this case, the event we are interested in is "at least 2 people having the same birthday". The complement of this event is "all 12 people having different birthdays".ย  ย Let's calculate the probability of all 12 people having different birthdays.The first person can have any birthday. The second person can have any birthday except the first person's birthday, so there are 364 options. The third person can have any birthday except the first two people's birthdays, so there are 363 options. And so on.Therefore, the total number of ways that 12 people can have different birthdays is:365 * 364 * 363 * ... * 354The total number of ways that 12 people can have any birthdays (regardless of whether they are the same or different) is:365^12So, the probability of all 12 people having different birthdays is:(365 * 364 * 363 * ... * 354) / (365^12)Now, using the complement rule, we can calculate the probability of at least 2 people having the same birthday:1 - (365 * 364 * 363 * ... * 354) / (365^12)This calculation can be done using a calculator. The answer is approximately 0.167, or 16.7%.

  • Replied 3 weeks ago

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    process There is a group of 12 people. Assuming there is no such concept of leap year, find out the probability of at least 2 people have the same birthday in a group

  • Replied 3 weeks ago

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    process There is a group of 12 people. Assuming there is no such concept of leap year, find out the probability of at least 2 people have the same birthday in a group