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 :

Total outcome = 365
1) 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...

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
P(2 born on same day) = 1- P( 2 not born on same day)
![\text{P(2 born on same day) }=1-[\frac{365}{365}\times \frac{364}{365}]](https://tex.z-dn.net/?f=%5Ctext%7BP%282%20born%20on%20same%20day%29%20%7D%3D1-%5B%5Cfrac%7B365%7D%7B365%7D%5Ctimes%20%5Cfrac%7B364%7D%7B365%7D%5D)
![\text{P(2 born on same day) }=1-[\frac{364}{365}]](https://tex.z-dn.net/?f=%5Ctext%7BP%282%20born%20on%20same%20day%29%20%7D%3D1-%5B%5Cfrac%7B364%7D%7B365%7D%5D)

The probability that among ten students in a class, at least two of them share a birthday is 0.002.
Answer with step-by-step explanation:
We are given that the recurrence relation

for n=5,6,7,..
Initial condition

We have to show that Fibonacci numbers satisfies the recurrence relation.
The recurrence relation of Fibonacci numbers
,
Apply this



Substitute n=2



Hence, the Fibonacci numbers satisfied the given recurrence relation .
Now, we have to show that
is divisible by 5 for n=1,2,3,..
Now replace n by 5n

Apply induction
Substitute n=1

It is true for n=1
Suppose it is true for n=k
is divisible 5
Let 
Now, we shall prove that for n=k+1 is true


It is multiple of 5 .Therefore, it is divisible by 5.
It is true for n=k+1
Hence, the
is divisible by 5 for n=1,2,3,..
Answer:
43.20
Step-by-step explanation:
Had to take one for the team
Answer:
2.1/√55
Step-by-step explanation:
simga divided by sample size