Arizona State University Engineering Probability and Statistics Questions I need someone to guarantee 100% for this assignment. So you have to write all an

Arizona State University Engineering Probability and Statistics Questions I need someone to guarantee 100% for this assignment. So you have to write all answers and scan and send it to me in one PDF file 1. [3 points)
(a) Define what we mean by the sample space of an experiment.
(b) Suppose an experiment consists of throwing together a coin and a dice. So one outcome
could be Heads, 3 and we write it as H3. List all elements of the sample space of this
experiment and what is the size of the sample space?
(c) Let A be the event of getting an odd number on the dice. List all elements in A.
(d) What is the probability of the event A?
(e) Let B be the event of getting a number higher than 5 on the dice. List elements of B.
(f) Compute the probability of B.
2. [3 points] Among 6 applicants for an open position, 4 are females and 2 are males. Suppose
three applicants are randomly selected from the applicant pool for final interviews. Find,
(a) the probability distribution of X, the number of female applicants among the chosen
three.
(b) the probability distribution of Y, the number of male applicants among the chosen three.
(c) What is the mean of the distribution of X?
3. [3 points) When rolling a die, let A denote the event consisting of outcomes {3,5}, and let
B denote the event consisting of outcomes {1, 2, 3). Determine,
(a) P(A)
(b) P(B)
(c) P(ANB);
(d) P(AB).
(e) P(AB).
(f) P(BA).
1
4. [3 points) Two firms X and Y consider bidding on a road-building job, which may or may not
be awarded depending on the amounts of the bids. Firm X submits a bid and the probability
is that it will get the job provided firm Y does not bid. The probability is that Y will
bid and if it does, the probability that X will get the job is only f.
(a) What is the probability that X will get the job?
(b) If X does not get the job, what is the probability that Y did not bid?
(c) If X does get the job, what is the probability that Y did bid?
5. [2 points] A quality-control engineer inspects a random sample of 5 batteries from a lot of
10 car batteries ready to be shipped. If such a lot contains 3 batteries with slight defects,
what is the probability that the inspector’s sample will contain
(a) none of the batteries with defects?
(b) exactly one of the batteries with defects?
(c) at least 2 batteries with defects.
6. [3 points] Given P(A) = 0.65, P(B) = 0.5, and P(ANB) = 0.25, find
(a) P(AUB);
(b) P?NB);
(C) P(ANB);
(d) P(AB)
() P(AB)
(f) P(BA)
(g) Are A and B independent?
7. [3 points) Two methods, A and B, are available for teaching a certain industrial skill. The
failure rate is 11% for A and 8% for B. However, B is more expensive and hence is used only
25% of the time. A worker is taught the skill by one of the methods.
(a) What is the probability that the worker learns it correctly?
(b) If he fails to learn it correctly, what is the probability that he was taught by method A?
(c) If he does learn it correctly, what is the probability that he was taught by method B?

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