If I have a 5% chance of catching a cold by hugging someone with a cold, what are the odds that I will catch a cold if I hug someone 150 times? Sorry, basic question.


This is a common question where calculating the inverse (not catching a cold) is much easier. The probability of not catching a cold when hugging someone is $0.95$, so the probability of not getting a cold after $150$ hugs is

$$0.95^{150} \approx 0.000455$$

The probability of catching a cold is one minus the probability of not catching a cold, so that is

$$1 - 0.95^{150} \approx 0.999544 = 99.9544\%$$

Conclusion: Don't hug too many people who have a cold!


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