Respuesta :

pingwin09
There are 365 out of 365 ways to select the birthday of first person. Therefore the number of ways that we can choose a birthday for second person is 364 out of 365. Until the fourth person is 362 out of 365. We use the "mutually exclusive event of probability" and the answer is (365/365)*(364/365)*(363/365)*(362/365) = 0.9836
ashutoshmishra3065

The probability that 4 randomly selected people all have different birthdays is [tex]0.984[/tex].

Probability

Probability is the ratio of the favorable outcomes to the total outcomes.

How to determine the probability?

There are 365 days in a year (non-leap year).

For first-person, the probability of birth date is [tex]\dfrac{365}{365}[/tex].

For the second-person, the probability of birth date is [tex]\dfrac{364}{365}[/tex] such that it should not match with other selected persons.

For the third-person, the probability of birth date is [tex]\dfrac{363}{365}[/tex] such that it should not match with other selected persons.

For the fourth-person, the probability of birth date is [tex]\dfrac{362}{365}[/tex] such that it should not match with other selected persons.

Hence, the probability that 4 randomly selected people all have different birthdays is-

[tex]P=\dfrac{365}{365}\times \dfrac{364}{365}\times \dfrac{363}{365}\times \dfrac{362}{365}\\=0.984[/tex]

Thus, the probability that 4 randomly selected people all have different birthdays is [tex]0.984[/tex].

Learn more about probability here- https://brainly.com/question/11234923

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