Determining if a Probability Question is Negative Binomial > Q: Suppose, David blinks with probability $0.2$ when the flash from a camera goes off. What is the probability that Roger, that's David's photographer, will need to take exactly $7$ individual photographs of David to have $3$ photographs without him blinking? I'm interpreting this question as a negative binomial situation. So far I have, $$Pr(X = 7) = \hspace{0.2cm} _6C_2(0.8)^3(0.2)^4 = 0.0123, \text{or } 1.23 \%$$ Is this interpretation correct? I feel like the answer is too small

It is a negative binomial question, but you can turn into a binomial question to check.

* The probability that two of the first six photographs do not have blinks is ${6 \choose 2}0.8^2 0.2^4$

* The probability that the seventh photograph does not have a blink is $0.8$

* Multiply these to get your result.




The number is small because it is far more likely to have more than three out of seven (or more than two out of six) without blinks