Let event G = taking a math class. Let event H = taking a science class. Then, G ∩ H = taking a math class and a science class while G ∪ H = taking either a math class or a science class. Suppose P(G) = 0.42, P(H) = 0.45, and P(G ∪ H) = 0.25. What is P(G ∩ H)

Given 2 events, A and B. Suppose P(A) =0.6 and P(B)=0.6. Which one of the following statements must be correct? Select one: O OO O O a Event A and Event B are the same event. b. Event A and Event B can not be mutually exclusive c. P(A and B) 0.6

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30% of students take Physics101 and 20% take Math146. Of the students who take Physics 101, 25% also take Math146. The events taking Physics 101 and Math146 are O a. independent O b. dependent O c. Disjoint d. None of the above

Let A and B be two events with P(A and Bc) = 1. Find P(B). Recall that Bc denotes the complement of the event B.

Determine whether the eventsare independent or dependent. Then find theprobability.  A computer program randomly assigns a letter from A to E and a number from 1 to 4 as a user's temporary password. The program assigns C2 as Rebecca's temporary password.

When randomly selecting adults, let M denote the event of randomly selecting a male and let B denote the event of randomly selecting someone with blue eyes.   What does P(M|B) represent? Is P(M|B) the same as P(BIM)?

Event E and event F are independent. Fiven P(E) = 0.3, P = (F) 0.5, compute P(E and F) and P(E or F). a) P(E and F) = b ) P(E or F)

Suppose that in a large university, 40% of students work part time, 10% are part of one of the university's sports teams, and 5% both work part time and are part of one of the university's sports teams. Let W be the event that a student works part time, and V be the event that a student is part of one of the university's sports teams. Make sure all your answers are expressed in terms of the events W and V,. 4. А. What is the probability that a randomly selected student works part time or is a part of one of the university's sports teams? В. teams? What proportion of students do not work part time but are part of one of the university's sports С. Are W and V independent events? D. If a student works part time, what is the probability they are also part of one of the university's sports teams? Е. What proportion of students are not part of any of the university's sports teams and work part time?