Given the following: A, B, and C are events. P[A] = 0.3 P[B] = 0.3 P[C] = 0.55 P[A intersect B] = 0 P[A' intersect B' intersect C'] = 0.1 P[A intersect C'] = 0.2 (i) Write a set expression for each of the following events a through d. (ii) Find the probability of the event. (Please show all work. Use venn diagrams if necessary). (a) At least one of the events A, B, or C occurs. (b) Exactly one...
3.) Given that P(A) = .5, P(B) = .4, and P(A and B) = 2, Find each of the following. A venn diagram may help) a. P(A or B) b. P(B) c. P(AB) d. P(BA) 4.) Event E and F have probabilities P(E) = .5,P(F) = 4, and P(E and F) = 2 a. Are E and F mutually exclusive? Explain your answer. b. Are E and Findependent? Explain your answer
Let ??~N(3, 9) and ?? = 5 ? ??. a) Find P(X > 2) b) Find P(?1 < Y < 3) c) Find P(X > 4|Y < 2) Please use an approximation to calculate the value of ?(x), where necessary
Find a. P(Z=1.32) b. P(Z>5) c. P(-1<Z<1) d. P(-2<Z<2) e. P(-3<Z<3) (c, d, and e form what is called the Empirical Rule. Look it up!) f. The 20th percentile of Z g. The z value with 5% area to its right. please show all work not just answers and do all of them please and thank you will rate high
False Question 3 (1 point) <Venn 5> There are 2 events: A, B with P(A)-0.5, P(B)-0.4, P(AUB)-0.7 Find P(A n B) Question 4 (1 point) Saved <Venn 2 There are 2 events: A, B with P(A)-Q5, P(B)-0.4, PAUB)-0.7
1. U = {1, 2, 3, 4, 5, … 10} A = {6,7,8,9,10} B = {1, 3, 5, 7, 9}, C = { 2, 4, 6, 8, 10} b) Find B’ c) Find A ∪ (B ∩ C) 2. Use Venn diagrams to show why A ∩ (B ∪ C) = (A ∩ B) ∪ (A ∩ C). 3. In a large class, there are 45 students who are either on a sports team or involved in an academic club...
5. In a given sample space, there are events A and B with P(A) .5, P(B)4, and P(AnB) (a) What is P(AU B)? (b) What is P(A'nB')? 6. In a given sample space, there are events C and D with P(C) .5 and P(D)-8. Given this information: (a) what is the largest value that PCnDcould possibly be? (b) what is the smallest value that P(Cn D) could possibly be? (hint: use Venn diagrams.) . A bowl contains 4 slips of...
5. Suppose A, B are events such that P(A) = 1/3, P(B) = 1/4, find P(AUB) under each of the following assumptions: (a) If A and B are mutually exclusive (disjoint). (b) If A and B independent.
4. 5 pts] Prove that P(A n B | C) = PAI B n C)P(B | C).
5. If 4 and B are mutualiy exclusive events and PA) 0.3 and PB)0.5. find (b) PA: INT Construct Venn diagrams and fill in the probabilities associated with the various regions. .. B. and C are mutually exclusive events and