Simulating Birthdays A student wants to conduct the simulation described in Example, but no calculator or computer is available, so the student uses 365 individual index cards to write the individual numbers between 1 and 365. The student then shuffles the cards, selects one, and records the result. That card is replaced, the cards are again shuffled and a second number is drawn. This process is repeated until 25 birthdays are generated. Does this simulation behave the same way as the process of selecting 25 people and recording their birthdays? Why or why not?
Yes. Since student uses 365 individual cards and every time he/she randomly select the card with replacement so each “birthday” has equally likely chance of being chosen for each of the 25 selections. Therefore this simulation behaves the same way as the process of selecting 25 people and recording the birthday.