Consider the following two probability distributions:Distribution A Distribution Bx P(x) x P(x)0 0.20 0 0.011 0.20 1 0.022 0.20 2 0.943 0.20 3 0.024 0.20 4 0.01Which of the following is an accurate statement regarding these twodistributions?a. Distribution A has a higher variance.b. Distribution B has a higher variance.c. Both distributions are positively skewed.d. Both distributions are uniform.30. Three boxes A, B and C contain screws. The probability of a screw being adefective in boxes A, B and C are 1/5, 1/6 and 1/7, respectively. A box is chosenat random and a screw is randomly selected from it. The screw was found to bedefective. What is the probability that the screw came from box A?a. 40/107b. 41/107c. 42/107d. 43/10731. A bag has 5 white marbles, 8 red marbles and 4 purple marbles. If we take amarble randomly, then what is the probability of not getting purple marble?

30. To solve this problem, we need to use Bayes' theorem. The probability that the screw came from box A given that it is defective is equal to the probability of a screw being defective in box A times the probability of choosing box A, divided by the total probability of getting a defective screw.

The probability of choosing any box is 1/3 (since there are three boxes). The probability of a screw being defective in boxes A, B, and C are 1/5, 1/6 and 1/7, respectively.

So, the total probability of getting a defective screw is (1/3)(1/5) + (1/3)(1/6) + (1/3)*(1/7) = 107/630.

Therefore, the probability that the screw came from box A given that it is defective is (1/3)*(1/5) / (107/630) = 42/107. So, the correct answer is c. 42/107.

31. The total number of marbles in the bag is 5 white + 8 red + 4 purple = 17 marbles. The probability of not getting a purple marble is the total number of marbles that are not purple divided by the total number of marbles.

So, the probability of not getting a purple marble is (5 white + 8 red) / 17 = 13/17.

As for the first question, we need to calculate the variance for each distribution. Variance is a measure of how spread out the numbers in a data set are. It is calculated as the average of the squared differences from the mean.

For Distribution A, all probabilities are the same, so it is a uniform distribution. Therefore, its variance will be lower. For Distribution B, the probabilities are not the same, and the probability for x=2 is much higher than for the other values, so the values are more spread out, and the variance will be higher. So, the correct answer is b. Distribution B has a higher variance.