Probability And Statistics | Week 2
Probability And Statistics Week 2 Answers
Link : Probability And Statistics (nptel.ac.in)
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?
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?
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?
(D) 5/21 – answered by ayush (comments)
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?
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?
Q6. Let X be a discrete random variable with the p.m.f. as
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?
Q8. A random variables X has the following probability mass functions
X 0 1 2 3 4 5
P(X=x) 0 2k 3k 2k2 4k 9k2+k
Find P(X < 3).
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?
(A) 1- P₁ …. Pn
(B) 1 – (1-P₁) … (1 – Pn)
(C) (1 – P₁) … (1 – Pn)
(D) P₁ …. 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 a high level of contamination?
The answer to ques 3 is option (d) by using the Bayes’ theorem
(1/6). (2/3 * 1/6) + (1/3 * 1/6) = 2/18 + 1/18 = 3/18 = 5/21