Respuesta :
When dealing with the union of two events, the formula states
[tex] P(A \cup B) = P(A) + P(B) - P(A \cap B) [/tex]
You need to subtract elements belonging to both A and B, otherwise you would count them twice.
So, the probability that a turbine will have defective blades and defective coil is
[tex] P(both defective) = 0.1 + 0.15 - 0.04 = 0.21 [/tex]
To compute the probability of non-defective turbines, you can use this strategy: if we divide the sample space in subsets with no intersections, then they form a partition of the sample space, and you have
[tex] P(\Omega) = P(A_1)+P(A_2) + \ldots + P(A_n) [/tex]
where [tex] \Omega [/tex] is the sample space, and each [tex] A_i [/tex] is a subset of the partition.
In this case, we can use the following partition:
[tex] A_1 = \{ \text{coil defective only} \},\quad A_2 = \{ \text{blades defective only}\},\quad A_3 = \{ \text{both defective} \},\quad A_4 = \{ \text{non-defective}\} [/tex]
So, we have
[tex] P(\Omega) = 1 = P(A_1)+P(A_2)+P(A_3)+P(A_4) [/tex]
And we are interest in [tex] P(A_4) [/tex], so we have
[tex] 1 - P(A_1) - P(A_2) - P(A_3) = P(A_4) [/tex]
Now, the turbines with only defective coil are those with defective coils and non-defective turbines:
[tex] P(A_1) = P(\text{defective coil}) - P(\text{both defective}) = 0.1 - 0.04 = 0.06 [/tex]
Similarly,
[tex] P(A_2) = P(\text{defective blades}) - P(\text{both defective}) = 0.15 - 0.04 = 0.11 [/tex]
We already know [tex] P(A_3) = 0.04 [/tex], so we can solve
[tex] P(A_4) = 1-0.06-0.11-0.04 = 0.79 [/tex]
The probability that a turbine will have one of these defects is 0.21 and the probability that a turbine will have neither of these defects is 0.79 and this can be determined by using the given data.
Given :
The probability that a turbine will have a defective coil is 0.10, the probability that it will have defective blades is 0.15, and the probability that it will have both defects is 0.04.
a) The probability that a turbine will have one of these defects is calculated as:
[tex]\rm P = P(A\cup B)[/tex]
[tex]\rm P = P(A)+P(B)-P(A\cap B)[/tex]
Now, substitute the values of the known terms in the above expression.
P = 0.10 + 0.15 - 0.04
P = 0.21
b) The probability that a turbine will have neither of these defects is calculated as:
[tex]\rm P =1- P(A\cup B)[/tex]
Substitute the value of the known term in the above expression.
P = 1 - 0.21
P = 0.79
For more information, refer to the link given below:
https://brainly.com/question/795909
