Questions: Based upon the pattern shown, what is the probability that 3 randomly selected individuals all share the same birthday? Assume that you're not one of the three people in the room.
Use the following website, https://wwwwolframalpha,com/2 you find the probability. Answer in scientific notation.
2.05647 × 10^-8
0.0000075
0.01271
Transcript text: Based upon the pattern shown, what is the probability that 3 randomly selected individuals all share the same birthday? Assume that you're not one of the three people in the room.
Use the following website, https://wwwwolframalpha,com/2 you find the probability. Answer in scientific notation.
$2.05647 \times 10^{\wedge}-8$
0.0000075
0.01271
Solution
Solution Steps
Step 1: Define the Problem
We want to find the probability that 3 randomly selected individuals all share the same birthday. We assume that there are 365 possible birthdays, and we denote the probability of success (all three individuals sharing the same birthday) as \( p = \frac{1}{365} \). The probability of failure (not sharing the same birthday) is \( q = \frac{364}{365} \).
Step 2: Apply the Binomial Probability Formula
The probability of exactly \( x \) successes in \( n \) trials can be calculated using the binomial probability formula: