A computer consulting firm presently has bids out on three projects. Let Ai = {awarded project i}, for i = 1, 2, 3, and suppose that P(A1) = .22, P(A2) = .25, P(A3) = .28, P(A1 ∩ A2) = .11, P(A1 ∩ A3) = .05, P(A2 ∩ A3) = .07, P(A1 ∩ A2 ∩ A3) = .01. Express in words each of the following events, and compute the
- a. A1 ∪ A2
- b. A1′∩ A2′ [Hint: (A1 ∪ A2)′ = A′1 ∩ A′2]
- c. A1 ∪ A2 ∪ A3
- d. A′1 ∩ A′2 ∩ A′3
- e. A′1 ∩ A′2 ∩ A3
- f. (A′1 ∩ A′2 ) ∪ A3
a.
Compute
Answer to Problem 13E
The probability of an event
Explanation of Solution
Given info:
The data represents the projects of the consulting firm.
Here, A1 be awarded project 1,
A2 be awarded project 2,
A3 be awarded project .
Let
Calculation:
Addition rule:
For any two events A and B,
Complement:
The complement of the event A contains the set of all element that are contained in sample space S and not contained in event A. it is denoted as
Union:
The union of two events A1 or A2 contains set of all elements which are either in A1, A2, or both the events. It is denoted by
Intersection:
The intersection of two event A1 and A2 contains set all of element which are in both A1 and A2. It is denoted by
The probability of A1 or A2 can be obtained as
Thus, the probability of an event
b.
Compute
Answer to Problem 13E
The probability of an event
Explanation of Solution
Calculation:
The probability of
The event
Thus, the probability of an event
c.
Compute
Answer to Problem 13E
The probability of an event
Explanation of Solution
Calculation:
Addition rule:
For any three events A, B and C ,
The event
The probability of
Thus, the probability of an event
d.
Compute
Answer to Problem 13E
The probability of an event
Explanation of Solution
Calculation:
The event
The probability of
Thus, the probability of an event
e.
Compute
Answer to Problem 13E
The probability of an event
Explanation of Solution
Calculation:
The event
The event
From the Venn diagram, the probability of
Thus, the probability of an event
f.
Compute
Answer to Problem 13E
The probability of an event
Explanation of Solution
Calculation:
The event
The event
The probability of
Thus, the probability of an event
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Chapter 2 Solutions
Student Solutions Manual for Devore's Probability and Statistics for Engineering and the Sciences, 9th
- 2. Suppose that in Example 2.27, 400 units of food A, 500 units of B, and 600 units of C are placed in the test tube each day and the data on daily food consumption by the bacteria (in units per day) are as shown in Table 2.7. How many bacteria of each strain can coexist in the test tube and consume all of the food? Table 2.7 Bacteria Strain I Bacteria Strain II Bacteria Strain III Food A 1 2 0 Food B 2 1 3 Food C 1 1 1arrow_forwardA computer consulting firm presently has bids out on three projects. Let Ai = {awarded project i}, for i = 1, 2, 3, and suppose that P(A1) = 0.23, P(A2) = 0.25, P(A3) = 0.29, P(A1 ∩ A2) = 0.08, P(A1 ∩ A3) = 0.05, P(A2 ∩ A3) = 0.07, P(A1 ∩ A2 ∩ A3) = 0.01. Use the probabilities given above to compute the following probabilities, and explain in words the meaning of each one. (Round your answers to four decimal places.) P(A1 ∩ A2 ∩ A3 | A1 ∪ A2 ∪ A3)arrow_forwardA computer consulting firm presently has bids out on three projects. Let Ai = {awarded project i}, for i = 1, 2, 3, and suppose that P(A1) = 0.22, P(A2) = 0.26, P(A3) = 0.28, P(A1 ∩ A2) = 0.07, P(A1 ∩ A3) = 0.09, P(A2 ∩ A3) = 0.08, P(A1 ∩ A2 ∩ A3) = 0.01. Use the probabilities given above to compute the following probabilities. (Round your answers to four decimal places.) (a) P(A2 ∩ A3 | A1) (b) P(A2 ∪ A3 | A1) Please use typefont and explain the steps clearly. Thank you!arrow_forward
- A computer consulting firm presently has bids out on three projects. Let A₁ = {awarded project /}, for i = 1, 2, 3, and suppose that P(A₂) = 0.23, P(A₂) = 0.26, P(A3) = 0.29, P(A₁A₂) = 0.11, P(A₁ A₂) = 0.05, P(A₂ A3) = 0.08, P(A₁ A₂ A3) = 0.01. Use the probabilities given above to compute the following probabilities, and explain in words the meaning of each one. (Round your answers to four decimal places.) (a) P(A₂|A₂₁) = Explain this probability in words. O This is the probability that the firm is awarded either project 1 or project 2. O This is the probability that the firm is awarded both project 1 and project 2. O If the firm is awarded project 1, this is the chance they will also be awarded project 2. O If the firm is awarded project 2, this is the chance they will also be awarded project 1. (b) P(A₂A₂A₂) = Explain this probability in words. O This is the probability that the firm is awarded at least one of the projects. O This is the probability that the firm is awarded projects…arrow_forwardA computer consulting firm presently has bids out on three projects. Let A; = {awarded project i}, for i= 1, 2, 3, and suppose that P(A₁) = 0.23, P(A₂) = 0.26, P(A3) = 0.28, P(A₁ A₂) = 0.08, P(A₁ A₂) = 0.07, P(A₂n A3) = 0.05, P(A₁ A₂ A3) = 0.02. Use the probabilities given above to compute the following probabilities, and explain in words the meaning of each one. (Round your answers to four decimal places.) (a) P(A₂|A₁₂) = | Explain this probability in words. O If the firm is awarded project 2, this is the chance they will also be awarded project 1. O This is the probability that the firm is awarded either project 1 or project 2. O If the firm is awarded project 1, this is the chance they will also be awarded project 2. O This is the probability that the firm is awarded both project 1 and project 2. (b) P(A₂n A3 A₁) =| Explain this probability in words. O This is the probability that the firm is awarded projects 1, 2, and 3. O This is the probability that the firm is awarded at least…arrow_forwardA computer consulting firm presently has bids out on three projects. Let Ai= {awarded project i}, for i = 1, 2, 3, and suppose that P(A1) = 0.22, P(A2) = 0.25, P(A3) = 0.28, P(A1 \cap A2) = 0.12, P(A1 \cap A3) = 0.04, P(A2 \cap A 3) = 0.05, P(A1 \cap A2 \cap A3) = 0.01. Compute the probability of each event.arrow_forward
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