An advertising campaign is canceled before launch with probability 0.10, in which case the marketing company is fired with probability 0.74; is launched but canceled early with probability 0.18, in which case the marketing company is fired with probability 0.43; is launched and runs its targeted length with probability 0.43, in which case the marketing company is fired with probability 0.16; and is launched and is extended beyond its targeted length with probability 0.29, in which case the marketing company is fired with probability 0.01. What is the probability that the marketing company is fired

0.2231 (22.31%)

Step-by-step explanation:

defining the event F = the marketing company is fired, then the probability of being fired is:

P (F) = probability that the advertising campaign is cancelled before lunch * probability that marking department is fired given that the advertising campaign was cancelled before lunch + probability that the advertising campaign is launched but cancelled early * probability that marking department is fired given that the advertising campaign is launched but cancelled early ... (for all the 4 posible scenarios where the marketing department is fired)

thus

P (F) = 0.10 * 0.74 + 0.18 * 0.43 + 0.43 * 0.16 + 0.29*0.01 = 0.2231 (22.31%)

then the probability that the marketing department is fired is 0.2231 (22.31%)