Question

If two people are selected at​ random, the probability that they do not have the same birthday​ (day and​ month) is startfraction 365 over 365 endfraction times startfraction 364 over 365 endfraction . explain why this is so.​ (ignore leap years and assume 365 days in a​ year.)

Answer 1

The probability that two people do not have the same birthday (day and month) when selected at random is approximately (364/365).

Step-by-step explanation:

The probability that two people do not have the same birthday (day and month) when selected at random can be calculated using the principle of complementary probability. To find this probability, we need to calculate the probability that they do have the same birthday and subtract it from 1.

Let's break down the process:

1. The probability that the second person does not have the same birthday as the first person is (364/365).
2. Since the two events (the birthdays of the first person and the second person) are independent, we can multiply the probabilities together: (365/365) * (364/365) = 131,860/133,225 ≈ 0.9878.

Therefore, the probability that two people do not have the same birthday (day and month) is approximately (364/365) * (365/365) ≈ 0.9878.

Answer 2

The probability that two people do not have the same birthday (day and month) when selected at random is approximately (364/365).

Step-by-step explanation:

The probability that two people do not have the same birthday (day and month) when selected at random can be calculated using the principle of complementary probability. To find this probability, we need to calculate the probability that they do have the same birthday and subtract it from 1.

Let's break down the process:

1. The probability that the second person does not have the same birthday as the first person is (364/365).
2. Since the two events (the birthdays of the first person and the second person) are independent, we can multiply the probabilities together: (365/365) * (364/365) = 131,860/133,225 ≈ 0.9878.

Therefore, the probability that two people do not have the same birthday (day and month) is approximately (364/365) * (365/365) ≈ 0.9878.

Answer 3

Because you have to times probability that the firs person is born on a day of the year (1/1,=365/365) by probability that the second one is born in another day (364/365).