What is the probability that two people selected at random have the same birthday? Ignore leap years.
To calculate the probability that two people selected at random have the same birthday, we need to consider the number of possible outcomes and the number of favorable outcomes
To calculate the probability that two people selected at random have the same birthday, we need to consider the number of possible outcomes and the number of favorable outcomes.
First, let’s determine the number of possible outcomes. Assuming there are 365 days in a year (ignoring leap years and assuming an equal likelihood for each day to be someone’s birthday), there are 365 potential birthdays for the first person and 365 potential birthdays for the second person.
Therefore, the number of possible outcomes is 365 * 365 = 133,225.
Next, let’s determine the number of favorable outcomes, which in this case is the number of ways both people could have the same birthday. Since there are 365 possible birthdays, the first person can have any of those 365 birthdays. Once the first person’s birthday is chosen, the second person also needs to have the same birthday. This leaves only one possibility.
Therefore, the number of favorable outcomes is 365 * 1 = 365.
Now we can calculate the probability by dividing the number of favorable outcomes by the number of possible outcomes:
Probability = Favorable Outcomes / Possible Outcomes
= 365 / 133,225
≈ 0.0027
≈ 0.27%
So, the probability that two people selected at random have the same birthday (ignoring leap years) is approximately 0.27%.
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