40. A container contains 3 red marbles, 7 green marbles and 10 white marbles. On the off chance that two marbles

are drawn from the container aimlessly, what is the likelihood that one marble is white

also, one is red?

41. A bite the dust is rolled. What is the likelihood that the number is even or under 4?

42. You move two 6-sided dice. What is the likelihood that the amount of the two dice is 10?

43. A distinguishing proof code is to comprise of seven letters followed by three digits. The number of

various codes are conceivable if redundancy is allowed?

44. A 8-bit parallel word is a grouping of 8 digits, of which each might be either a 0 or a 1.

What number of various 8-bit words are there?

45. Jane and Thomas are among the 8 individuals from which an advisory group of 4 individuals is to

be chosen. The number of various potential advisory groups of 4 individuals can be chosen from

these 8 individuals if at any rate one of either Jane or Thomas is to be chosen?

46. Georgia tags comprise of three letters followed four numbers. The number of permit

plate mixes are conceivable if the tag contains no vowels (A, E, I, O, U,

or on the other hand Y) nor contains the number 5.

47. Given that there are four characters (Adenine, Guanine, Cytosine,Thymine) in 25

character strand of DNA, what is the opportunity that a poly-atail of 25 adenines

can happen in succession on the off chance that they happen arbitrarily in nature?

48. You eleven tile letters PENULTIMATE are in a sack. Discover the likelihood that, if 8

letters are drawn aimlessly and set down all together, "extreme" is spelled?

49. A reasonable spinner has four similarly separated shading areas (blue, red, green, and yellow).

What is the likelihood that the spinner will arrive on green?

50. A urn contains 5 red, 3 green, and 4 yellow marbles. A marble is haphazardly picked

from the urn. The marble is supplanted in the urn, and a subsequent marble is picked. What

is the likelihood of picking a red and afterward a purple marble?

51. A class has 4 young men and 12 young ladies. They are haphazardly partitioned into 4 gatherings of 4. What

is the likelihood that each gathering has 1 kid?

An article in the Journal of the American Statistical Association [\"Illustration of Bayesian Inference in Normal Data Models Using Gibbs Sampling\" (1990, Vol. 85, pp. 972985)] measured the weight of 30 rats under experiment controls. Suppose that 12 were underweight rats. 1 . Calculate a 95% two-sided condence interval on the true proportion of rats that would show underweight from the experiment. 2. Using the point estimate of p obtained from the preliminary sample, what sample size is needed to be 95% condent that the error in estimating the true value of p is less than 0.02? 4.2 Bayesian Inference (15 points) A man goes fishing to 3 different lakes: L1, L2, and L3. Because of varying difficulty in getting to the lakes, he visits the lakes with probabilities: P(L1) = 0.7, P(L2) = 0.2, and P(L3) = 0.1. Each lake contains the same 4 species of fish: carp, tench, pike and perch. The man stays at the lake until he has caught exactly 4 fish. The probabilities of a fish belonging to each species from each lake are as follows: P(carp L1) = 0.1, P(tench| L1) = 0.6, P(perch L1) = 0.2, P(pike| L1) = 0.1A random variable X is uniformly distributed over the interval [0, B]. The parameter E is unknown, and it is modeled as the value of a random variable Y 1ilvhich is uniformly.r distributed on the interval [[1, 1]. Assuming that X is measured at the value it, use Bayes rule to update the distribution of Y. Hirrt: since X is corrtinuous you should use the odf of X for the likelihood function. The Bayesian inference formula is: mall") = f'3'8;f\"(8] where x|BII 2 pdf of X at the point x for parameter value B, and where Z is the evidence 3 = f Itzlemlelde