Problem 7) Consider the interval S = [-1,2]. Suppose a number x is equally likel
ID: 3303731 • Letter: P
Question
Problem 7) Consider the interval S = [-1,2]. Suppose a number x is equally likely to be {x1 1x-0.41 0.5), and selected in S. Consider the events A = {xlx 0.75). Find the probabilities of A, B, and C? Find the probabilities of A UB, A U C, and AUBUC? a) b) Problem 8) Consider the previous problem again. Suppose the number x is twice more likely to be selected in -1,0] than in (0,2]. a) Propose a probability law for this sample space. b) Consider events A, B, and C in the previous problem. Find the probabilities of A, B, and C? c) Find the probabilities of A U B, A U C, and AUBUC?Explanation / Answer
Problem 7.
In order to solve this we need to first find out total number of elements in sample space. Lets divide the sample space using 0.05
There will be total 61 different numbers in S = [-1,2] including both.
n(S) = 61
n(A) = 20
For event B, values ranging from -0.1 to 0.9 will be the elements. n(B) = 21
n(C) = 25
(a)
P(A) = 20/61 = 0.3279
P(B) = 21/61 = 0.3443
P(C) = 25/61 = 0.4098
(b)
n(A U B) = n(A) + n(B) - n(A and B) = 20 + 21 - 2 = 39
P(A U B) = 39/61 = 0.6393
n(A U C) = n(A) + n(C) - n(A and C) = 20 + 25 - 0 = 45
P(A U C) = 45/61 = 0.7377
P(A U B U C) = 1 (as all numbers are covered by 3 events)