Question

b. if four people are selected at random, find the probability that they all have different birthdays. the probability that they all have different birthdays is (round to three decimal places as needed.)

Explanation:

Step1: Calculate total possible birthday combinations

Each person can have a birthday on one of 365 days (ignoring leap - years for simplicity). So for 4 people, the total number of possible birthday combinations is $n = 365\times365\times365\times365=365^{4}$.

Step2: Calculate number of combinations with different birthdays

The first person can have a birthday on 365 days. The second person must have a birthday on a different day, so there are 364 choices. The third person has 363 choices and the fourth person has 362 choices. So the number of combinations with different birthdays is $m=365\times364\times363\times362$.

Step3: Calculate the probability

The probability $P$ that all 4 people have different birthdays is $P=\frac{m}{n}=\frac{365\times364\times363\times362}{365^{4}}$.

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Answer:

0.986