Assume there are 365 days in a year.What is the probability that ten students in a class have different birthdays?What is the probability that among ten students in a class, at least two of them share a birthday?

Answer:1) The probability that ten students in a class have different birthdays is 0.883.2) The probability that among ten students in a class, at least two of them share a birthday is 0.002.Step-by-step explanation:Given : Assume there are 365 days in a year.To find : 1) What is the probability that ten students in a class have different birthdays?2) What is the probability that among ten students in a class, at least two of them share a birthday?Solution : [tex]\text{Probability}=\frac{\text{Favorable outcome}}{\text{Total number of outcome}}[/tex]Total outcome = 3651) Probability that ten students in a class have different birthdays is The first student can have the birthday on any of the 365 days, the second one only 364/365 and so on...[tex]\frac{364}{365}\times \frac{363}{365} \times \frac{362}{365} \times \frac{361}{365}\times\frac{360}{365} \times \frac{359}{365} \times \frac{358}{365} \times \frac{357}{365} \times\frac{356}{365}=0.883[/tex]The probability that ten students in a class have different birthdays is 0.883.2) The probability that among ten students in a class, at least two of them share a birthdayP(2 born on same day) = 1- P( 2 not born on same day)[tex]\text{P(2 born on same day) }=1-[\frac{365}{365}\times \frac{364}{365}][/tex][tex]\text{P(2 born on same day) }=1-[\frac{364}{365}][/tex][tex]\text{P(2 born on same day) }=0.002[/tex]The probability that among ten students in a class, at least two of them share a birthday is 0.002.