Probability Theory and Probability Distribution - Statistics Assignment Help

Assignment Task

Q1.

a. How many 4 digit numbers be formed by using digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9

(i) When each digit used once.

(ii) When repetition is allowed.

b. A bag containing 7 different balls. Three balls are drawn at random, (i) with replacement (ii) without replacement. How many drawings are possible?

c. How many number plates of 2 alphabets followed by 4 digits be formed?

Q2.

a. A card is drawn from a deck of 52 cards, what is the probability that

(i). a king. (ii) a diamond. (iii) a face card. (iv). A diamond or a 9. (v). a black card

b. A machine fills packets of chips 3% of the time it underfills and 2% times it overfills the packets. What is the probability that a packet randomly selected is either underfilled or overfilled?

Q3

a) From a group of 3 Statisticians, 4 Economists and 4 Physicists, a committee of 3 persons is to be selected. Find the probability that the selected committee will base

i) 2 Economists

ii) At least 2 Economists (Hint: combinational probability)

b) There are 30 boys and 20 girls in a class. 20 boys and 10 girls use their own transport to reach the collage. If a student is selected at random, find the probability that the student selected is a boy or a student using his or her own transport o reach the collage?

Q4 A census of a company’s 500 employees in regard to a certain proposal revealed that 125 of its 150 white-collar workers are in favor of the proposal and a total of 125 workers opposed the proposal. All workers can be classified as either white collar or blue collar.

Find the probability that an employee selected at random he is,

a) A white-collar worker and against the proposal

b) In favor of proposal

c) In favor of the proposal if he is a blue-collar worker

d) Either a white-collar worker or blue-collar worker is in favor of the proposal

Q5. A manufacturing company purchases a certain part of a machine from 3 suppliers A, B, and C. Supplier A supplies 60% of the parts. Supplier B supplies 30% and C supplies 10%. The defective parts supplied by A, B and C are known to be 0.25%, 1% and 2% respectively. During production process a defective part is found. What is the probability that it is from supplier

i) A

ii) B

iii) C

(Hint: first calculate probability of defective part by each supplier P(D/A, B and C respectively) and then P(A and D) and in the last place solve for P(D/A))

Q6.

a) Both engines on a small airplane fail, given that each engine fails with probability 0.05 and that an engine is twice as likely to fail when it is the only engine working

b) An automobile is recalled for brake failure and has steering problems, given that 15 % of that model were recalled for brake failure and 2 % had steering problems.

c) A citizen files his or her tax return and cheats on it, given that 70% of all citizens file returns and 25% of those who file cheat.

Q7.

a) The probability that a student passing a certain exam is ¾. Find the probability that in the group of 8 students only 3 will pass the examination?

b) A company vendor knowing that the vendor’s manufacturing process produces 0.005 defective parts. What is the probability that the company will receive at most 3 defective parts from a lot of 20,000 parts?

c) Suppose that the chance that a certain type of seed does not germinate is 4%. If 50 such seeds are planted, then what is the probability that 3 or fewer seeds do not germinate?

Q8.

a. What is the expectation of Ali who wins Rs. 10 when a fair coin tossed and head appears and losses Rs. 9 when tails appear?

b. The probability that any given machinery owned by a firm will required a major repair is 0.02. The firm has 10 machineries. What is the probability that more than 4 machines required a major repair?

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