Please , answer all of these questions. A satellite system consists of 3 compone
ID: 3181364 • Letter: P
Question
Please , answer all of these questions.
A satellite system consists of 3 components and functions on any given day if at least 2 of its 3 components function on that day. On a rainy day, each of the components independently functions with probability 0.6, whereas on a dry day they each independently function with probability 0.8. a) What is the probability that the satellite system will function on a rainy day? b) Let the probability of having a rainy day be 0.3 what is the probability that the satellite system will function on a random day? c) suppose we do not know yesterday's weather conditions but we know that the satellite was working. Given this fact, what is the probability that yesterday was rainy?Explanation / Answer
a) P(satellite system will function on a rainy day) = P(at least 2 out of 3 componets working on a rainy day) = P(2 componets working on a rainy day) + P(3 componets working on a rainy day)
= 3 x 0.6x0.6x0.4 + 0.63
= 0.648
b) P(satellite system will function on a dry day) = = P(at least 2 out of 3 componets working on a dry day) = P(2 componets working on a dry day) + P(3 componets working on a dry day)
= 3x0.8x0.8x.2 + 0.83
= 0.896
P(satellite working on a given day) = 0.3x0.648 + 0.7x0.896 = 0.8216
c) P(rainy | satellite was working) = 0.3x0.648/0.8216 = 0.2366