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Brain Teaser:
If there are 30 people in a room, what is the chance that at least two of them share a birthday?
Answer:
An easier question to answer is what is the chance that no two share a
birthday. For a group of three people, the probability is calculated as follows:
Give the first person any one of 365 days, the second person now has 364 days to choose from,
and the third person will have 363 days to choose from without having a repeat. The probability
that in a group of 3 no two will share a birthday is 365/365 * 364/365 * 363/365 = 99.18%
To solve for 30 people, simply extend this pattern thirty steps:
365/365 * 364/365 * 363/365 * ... 337/365 * 336/365 = 29.36%. So, the probability that
two people share a birthday is 100% - the probability that they don't share a birthday,
or 100% - 29.36% = 70.63%
Condition Probability Data Sheet
- Download Printable Data Sheet
- Place 2 Brown, 2 Red, 2 Yellow, and 2 Green M&Ms in a bag.
- Draw a M&M out of the bag. DO NOT put it back in the bag.
- Locate the Row with that color.
- Draw another M&M out of the bag.
- Locate the Column with that color.
- Place a tally mark in that cell.
- Replace both M&Ms.
- Repeat the process the desired number of times.
| | Second M&M |
| | Brown | Red | Yellow | Green |
| First M&M | Brown |
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| Red |
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| Yellow |
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| Green |
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