Discrete Mathematics Answers

Q NO.9 (Law of Total Probability) A production house owns three machines. Machine I, machine ii and machine iii, produces 25%, 30% and 40% of output. 5%, 4% and 2% of the output are observed to be defective. Worker draws a random product from the production. What is the probability of product being defective? Q NO.10 (Bayes’ Theorem)A = {x: x N, x < 6} B = {x: x N, 4 < x < 10} Find P (A / B). Q NO.11 (Bayes’ Theorem) Container I incorporate 2 tape balls and 3 footballs. Container 2 incorporates 4 tape balls and 1 football. ContainerIII incorporates 3 tape balls and 4 footballs. A cube having 3 pink, 2 yellow and one green-face, is thrown to choose the container. If pink face turns up, we select up container I, if a yellow face turns up we select up container II, otherwise, we select up container III. Then, we randomly pick a ball from the chosen container. If the ball drawn is tape ball, what’s the probability that the cube had become up with a pink face

Q NO.1 A sequence of 10 bits is randomly generated. What is the probability that at least one of these bits is 0? Q NO.2 What is the probability that a positive integer selected at random from the set of positive integers not exceeding 100 is divisible by either 2 or 5? Q NO.3 If you roll two dices. A: The Sum is at least 8. B: A double is rolled. Find, 1) P(A) 2) P(B) 3) P(B/A) Q NO.4 What probabilities should we assign to the outcomes H (heads) and T (tails) when a fair coin is flipped? What probabilities should be assigned to these outcomes when the coin is biased so that heads comes up twice as often as tails? Q NO.5 A bit string of length four is generated at random so that each of the 16-bit strings of length four is equally likely. What is the probability that it contains at least two consecutive 0s, given that its first bit is a 0? (We assume that 0 bits and 1 bit are equally likely.) Q NO.6 In a group of 8 students what is the probability that a. Nobody has a birthday on the same date.

Determine whether these system specifications are consistent: “The message is stored in the buffer, or it is retransmitted.” “The message is not stored in the buffer.” “If the message is stored in the buffer, then it is retransmitted.”