# Probability that the 10th class this semester is the 3rd class cancelled when chances are independent with 0.05 probability each day?

Every day, a lecture may be cancelled due to inclement weather with probability 0.05. Class cancellations on different days are independent. Compute the probability that the tenth class this semester is the 3rd class cancelled?

This is a practice exam so the exact answer isn't near as important as the proper solution. My assumption is P(3rd cancelled is 10th class) = P(2 cancellations in 9 classes)*P(cancelled)

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## 1 Answer

The procedure you propose is correct.

Call a cancelled class a success. So we want the probability of exactly $2$ successes in $9$ trials, followed on the $10$-th trial by a success.

The probability of success is $p=0.05$. So the probability of exactly $2$ successes in $9$ trials is $\dbinom{9}{2}p^2(1-p)^7$.

Multiply by $p$ to get the desired probability.

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