Question

What is the probability that 4 randomly selected people all have different birthdays? Ignore leap years, and round your final answer to four decimal places.
0.9729



0.9918



0.9891



0.9836

Answer 1

Answer:

(D)0.9836

Step-by-step explanation:

There are 365 days in a year.

Since each person has a different birthday:

• We can choose a birthday for the first person 365 out of 365 days.
• We can choose a birthday for the second person 364 out of 365 days.
• We can choose a birthday for the third person 363 out of 365 days.
• We can choose a birthday for the fourth person 362 out of 365 days.

Therefore,

P(4 randomly selected people all have different birthdays)

$=\dfrac{365}{365} \times \dfrac{364}{365} \times \dfrac{363}{365} \times \dfrac{362}{365}\\\\=0.9836$