For at least 6 pictures she must take to have at least a 4/5 chance of having a picture in which everyone is looking at the camera.
Let p define the probability of success in a Bernoulli trial, and P define the probability Sara wants to reach "at least" and n be defined as the number of trials. Then,
= 1 - (1 - p)ⁿ ≥ P
= (1 - p)ⁿ ≤ 1 - P
= n ≥ ln(1-P)/ln(1-p)
= n ≥ ln (0.2) / ln (0.75)
=5.6
Hence for at least n=6 photos, there is at least a chance of 4/5 that everyone is looking at the camera.
To learn more about probability and its theorem,
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