1111

1/2 * 1/2 * 1/2 * 1/2 = 1/2^4 = 1/16
1 - 1/16 = 15/16

(probability)^number_of_positive_detections = likelyhood_fraction

likelyhood_fraction^(1/number_of_positive_detections) = probability

1/(likelyhood_fraction^(probability)) = number_of_positive_detections