# Find the Probability that of 25 Randomly Selected Students, at Least Two, Share the same Birthday.

We will be using the concept of probability to solve this.

## Answer: The Probability that of 25 Randomly Selected Students, at Least Two, Share the same Birthday is 0.5687.

Let's solve this step by step.

**Explanation: **

Given that, there are 25 randomly selected students.

Probability (at least 2 shares the same birthday) = 1 - P(none of them hare same birthday)

P(at least 2 shares the same birthday) = 1 - (all different birthday ways)/(total number of ways)

Let us assume that there are 365 days in a year.

As anyone can have his birthday out of 365 days, the total number of ways = (365)^{25}

To give each one a different birthday, we can let everyone choose a birthday as his/her turn comes.

The first will have 365 choices, and the second will have 364 choices, the third will have 363 choices, and so on...,

The last will have 341 choices.

⇒ All different birthday ways = 365 × 364 × 363 × ... × 341

P(at least 2 shares the same birthday) = 1 - [365 × 364 × 363 × ... × 341 /(365)^{25}]

P(at least 2 shares the same birthday) = 1 - 0.4313

P(at least 2 shares the same birthday) = 0.5687

### Hence, The Probability that of 25 Randomly Selected Students, at Least Two, Share the same Birthday is 0.5687.

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