Final answer:
The probability of at least two people sharing a birthday in a room of 14 can be calculated using complementary probability and is approximately 0.248.
Step-by-step explanation:
The probability of at least two people in a room of 14 sharing a birthday can be calculated using the concept of complementary probability. To find the probability of no one sharing a birthday, we need to calculate the probability of each person having a different birthday.
The probability of a person having a different birthday from the rest is given by: 364/365, 363/365, 362/365, ..., 351/365. To find the total probability, we multiply all these probabilities together.
The probability of at least two people sharing a birthday can then be found by subtracting the probability of no one sharing a birthday from 1. The probability of at least two people sharing a birthday is approximately 0.248.