Question

Question 2. To determine

1. What probability distribution for birthday’s should be used to reflect how often February$\mathbf{29}$occurs?
2. What is the probability that in a group of$\mathit{n}$people at least two have the same birthday using the probability distribution from$\mathit{a}$?

Short answer

Answer

1. The probability of being born on February$29$ is$\frac{1}{1461}$.
2. The conditional probability is$0.706$

Step-by-step solution

Step 1. Given information 

February$29$ occurs only I leap years. Years divisible by $4$,but not by$100$ , are always leap years. Years divisible by $100$, but not by$400$ , are not leap years, but years divisible by $400$are leap years.

Step 2. Definition and formula to be used

Probability deals with the random event.

Step 3. a) Compute the probability

Leap year occurs once in $4$years. $4$years equals $1461$ days. Adding $1$of leap year makes it $1461$. So , the probability of being born on February $29$is.$\frac{1}{1461}$

The probability of being born on February $29$is $\frac{1}{1461}$.