Birthday Problem You are in a class that has 24 students. You want to find the probability that at least two of the students share the same birthday.

(a) First, find the probability that each student has a different birthday. 24 factors P(different birthdays) 365 364 363 362 365 365 365 365 343 342 365 365

(b) The probability that at least two students have the same birthday is the complement of the probability in part (a). What is this probability?

(c) We used a technology tool to generate 24 random numbers between 1 and 365. Each number represents a birthday. Did we get at least two people with the same birthday? 228 348 181 317 81 183 52 346 177 118 315 273 252 168 281 266 285 13 118 360 8 193 57 107

(d) Use a technology tool to simulate the "Birthday Problem." Repeat the simulation 10 times. How many times did you get at least two people with the same birthday?The Multiplication Rule and Conditional Probability By rewriting the formula for the Multiplication Rule, you can write a formula for finding conditional probabilities. The conditional probability of event B occurring, given that event A has occurred, is In Exercises 41 and 42, use the following information. • The probability that an airplane flight departs on time is 0.89. • The probability that a flight arrives on time is 0.87. • The probability that a flight departs and arrives on time is 0.83.