Determine the probability that at least 2 people in a room of 10 people share th

Question

Determine the probability that at least 2 people in a room of 10 people share the same birthday, ignoring leap years and assuming each birthday is equally likely, by answering the following questions: Compute the probability that 10 people have different birthdays. The complement of "10 people have different birthdays" is "at least 2 share a birthday". Use this information to compute the probability that at least 2 people out of 10 share the same birthday. The probability that 10 people have different birthdays is . (Round to four decimal places as needed.)

Explanation / Answer

PROBABILITY OF HAVING SAME BDAY = 1/365

PROBABILITY OF HAVING DIFFERENT BDAY = 364/365

A) NOW THE PROBABILITY THAT ALL 10 HAVE DIFFERENT BDAY = (364/365)^10 = 0.972

B) PROBABILITY THAT AT LEAST 2 HAVE SAME BDAY = 1 - P(NO SAME BDAY) ( AS ONLY 0 WILL BE COUNTED BACUASE TO SHARE AT LEAS 2 PEOPLE ARE REQUIRED)

PROBABILITY = 1 - 0.972 = 0.228

Related Questions

Navigate

• Browse (All)
• Browse D
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.