Solution Found!
The following table lists the history of 940 orders for
Chapter 2, Problem 219SE(choose chapter or problem)
The following table lists the history of 940 orders for features in an entry-level computer product.
Let 𝐴 be the event that an order requests the optional high-speed processor, and let 𝐵 be the event that an order requests extra memory. Determine the following probabilities:
(a) \(P(A \cup B)\)
(b) \(P(A \cap B))
(c) \(P\left(A^{\prime} \cup B\right)\)
(d) \(P\left(A^{\prime} \cap B^{\prime}\right))
(e) What is the probability that an order requests an optional high-speed processor given that the order requests extra memory?
(f) What is the probability that an order requests extra memory given that the order requests an optional high-speed processor?
Equation transcription:
Text transcription:
P(A cup B)
P(A cap B)
P(A^{prime} cup B)
P(A^{prime} cap B^{prime})
Questions & Answers
QUESTION:
The following table lists the history of 940 orders for features in an entry-level computer product.
Let 𝐴 be the event that an order requests the optional high-speed processor, and let 𝐵 be the event that an order requests extra memory. Determine the following probabilities:
(a) \(P(A \cup B)\)
(b) \(P(A \cap B))
(c) \(P\left(A^{\prime} \cup B\right)\)
(d) \(P\left(A^{\prime} \cap B^{\prime}\right))
(e) What is the probability that an order requests an optional high-speed processor given that the order requests extra memory?
(f) What is the probability that an order requests extra memory given that the order requests an optional high-speed processor?
Equation transcription:
Text transcription:
P(A cup B)
P(A cap B)
P(A^{prime} cup B)
P(A^{prime} cap B^{prime})
ANSWER:Solution :
Step 1 of 6:
Given the total number orders is 940.
Let A and B be the two events.
A = order requests the optional high speed processors.
B = order requests extra memory.
Then the table is given below.
Extra Memory |
|||
No |
Yes |
||
Optional high-speed processor |
No |
514 |
68 |
Yes |
112 |
246 |
|
Our goal is:
We need to find :
a). P(AB).
b). P(AB).
c). P().
d). P().
e). We need to find the probability that an order request an optional-speed processor given that the order requests extra memory or P.
f). We need to find the probability that an order request extra memory given that the order requests an optional high speed processor or P.
a). Now we have to find P(AB).
From the above table P(AB) is
P(AB) =
P(AB) =
P(AB) = 0.4531
Therefore, P(AB) = 0.453.