Emma decides to mix grades of gasoline in her truck. She puts in 6 gallons of regular and 14 gallons of premium for a total cost
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Answer:
P(X = 0) = 0.0208, P(X = 1) = 0.2484, P(X = 2) = 0.7308
Step-by-step explanation:
Let's define the following events
A: the first component meet specification
B: the second component meet specification
P(A) = 0.87
P(B) = 0.84
Let X be the random variable that represents the number of components in the assembly that meet specifications. Because there are only two mechanical components in the assembly, X can only take the values 0, 1, 2.
P(X = 0) = P(the first component does not meet specification and the second component does not meet specification) =
(because of independence)
= (0.13)(0.16) = 0.0208
P(X = 1) = P(only one component meet specification) = P[(the first component meet specification and the second component does not meet specification) or (the first component does not meet specification and the second component meet specification)] =
(because sets are mutually exclusive)
(because of independence)
= (0.87)(0.16) + (0.13)(0.84) = 0.2484
P(X = 2) = P(both components meet specifications) =
(because of independence)
= (0.87)(0.84)
= 0.7308