Question

Find the probability that 3 randomly selected people all have the same birthday. ignore leap years. round to eight decimal places.\

Answer 1

Answer:

Probability that 3 randomly selected persons have same birthday = 0.00820417

Step-by-step explanation:

Probability that 1 person has different birthday = 1

$\text{Probability that 2nd person has different birthday than 1st = }\frac{364}{365}\\\\\text{Probability that the 3rd person has different from 1st and 2nd = }\frac{363}{365}$

$\text{Probability that the all three persons have different birthday = }1\times \frac{364}{365}\times \frac{363}{365}\\\\=0.99179583$

The probability that all three persons have same birthday = 1 - 0.99179583

                                                                                                 = 0.00820417

Hence, probability that 3 randomly selected persons have same birthday = 0.00820417

Answer 2

The probability the 1st person has a birthday is 365/365 = 1
The probability the 2nd person has a DIFFERENT birthday is 364/365 = 0.9972603
The probability the 3rd person also has a DIFFERENT birthday is 364/365 = 0.9972603
 

the probability that they all have the same birthday is

1 - (0.9972603)(0.9972603) = 0.00547189