I have provided probable answers for all 10 quiz questions for week 2’s assignment. I encourage you to utilize these hints as a guide and complete the assignment before the deadline for submission.
Probability and Statistics NPTEL Assignment – WEEK 2
Q1.Two cards are drawn successively from a pack without replacing the first. If the first card is spade, then what is the probability that the second card is also a spade?
Answer: (C) 4/17
Q2. Four of the seven balls in a box have odd numbers on them. What is the probability that all three balls picked at random, one after the other, without replacement, have odd numbers?
Answer: (B) 4/35
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Q3.Two urns contain respectively 2 white and 1 black balls, and 1 white and 5 black balls. One ball is transferred from the first to the second urn, and then a ball is drawn from the second urn. What is the probability that the ball drawn is white?
Answer: (D) 5/21
Q4.There are 2 boxes: Box-1 contains 3 silver spoons and 3 copper spoons and Box-2 contains 5 copper and 3 silver spoons. Assume that Box-1 is likely to be chosen with a probability of 2/3 and Box-2 is likely to be chosen with a probability of 1/3. A spoon is chosen at random from a box that has been randomly selected. What is the probability that it is a silver spoon?
Answer: (A) 11/24
Q5) The chance that a certain disease is diagnosed correctly is 60%. The chance that the patient will die under the treatment, after correct diagnosis is 40%; and the chance of death by wrong diagnosis is 70%. A patient who had the disease died. What is the probability that his / her disease was diagnosed correctly?
Answer: (B) 6/13
Q6.Let X be a discrete random variable with the p.m.f. as
Answer: (C) 2/9
Q7.It is known that 2.5% of mobile phone chargers fail during the warranty period provided they are kept dry. The failure percentage is 5.6, if they are ever wet during the warranty period. If 91% of the chargers are kept dry and 9% are wet during warranty period, what is the probability that a phone charger fails during the warranty period?
Answer: (D) 0.0278
Q8.A random variables X has the following probability mass functions
Answer: (C) 0.455
Q9.Suppose the probabilities of n mutually independent events are P1, P2, Pn respectively. Then what is the probability that at least one of the events will occur?
Answer: (B) 1 – (1-P1)…(1-Pn)
Q10. Some elements in a chemical laboratory are highly contaminated. A high amount of contamination in an element is likely to exist with a 0.1 probability. The levels of contamination are evaluated on four randomly chosen elements. How likely is it that at least one of them has high level of contamination?
Answer: (C) 0.6561
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