Thread: Probability and statistics

In a night exercise three platoons, A,B,C are required to cross a stretch of ground in one hour without making so much noise that they are detected by the adjudicating officer. The platoons draw lots for the starting line times of the mid-night, 1.00 and 2.00, the best platoons, A, has the probability 3/4 of crossing sufficiently quietly while B,C have probabilities 1/2 and 1/4 of doing so. If the adjudicating officer hears no noise in the first hour, but some noise in each of the next two hours, what is the probability that the platoons crossed in alphabetical order?

Originally Posted by samuel2012

In a night exercise three platoons, A,B,C are required to cross a stretch of ground in one hour without making so much noise that they are detected by the adjudicating officer. The platoons draw lots for the starting line times of the mid-night, 1.00 and 2.00, the best platoons, A, has the probability 3/4 of crossing sufficiently quietly while B,C have probabilities 1/2 and 1/4 of doing so. If the adjudicating officer hears no noise in the first hour, but some noise in each of the next two hours, what is the probability that the platoons crossed in alphabetical order?

We must make an assumption not given, namely that the crossings are independent.
We are given that two of the crossings are 'noisy'.
Let's use to mean that platoons A has a quite crossing, and to mean that platoons B has a noisy crossing.

Here is what we are given

Now

Now your turn.