For two events A and B, P(A)=0.24, P(B)=0.57, and P(A∩B)=0.32. a.Find P(A|B) b. Find P(B|A) c. Are A and B are independent?

(b) 6 + 7 + 8 + 9 + .. + k

Find the following expressions if a = (6r, 0, r), b = (6s, –s, 7s), and c = (2t, 10t, 5). a ·b = 1. 2. a·c = 3. b.c =

If a = (-6, 12, -9), b = (2, -16, 18), and c = (28, -14, 3), what is 3. 6+2c? 2 %3D %3D (51, 0, -24) (57, -48, 30) (24, -18, 12) (20, 14, -24) C.

In an experiment with three conditions, the means are 2, 4, and 9. What would be the value of L for the coefficients 2, -1, -1?

When will n(A ∩ B) = 0? Explain and give an example.

At a sporting event, cheerleaders will throw 50 bundled T-shirts into the crowd. The T-shirt sizes consist of10 small, 15 medium, and the remainder either large or extra large. Suppose Ana catches a T-shirt. What is theprobability that she will catch a T-shirt that is not a size small? (A) (B) (C) (D) (E) 0.100.200.500.670.80

Let A5 = {5k|k € N}, A7 = {7k|k € N} Show that A5 A7 = 0

Allergic reactions to poison ivy can be miserable. Plant oils cause the reaction. Researchers at Allergy Institute did a study to determine the effects of washing the oil off within 5 minutes of exposure. A random sample of 1000 people with known allergies to poison ivy participated in the study. Oil from the poison ivy plant was rubbed on a patch of skin. For 500 of the subjects, it was washed off within 5 minutes. For the other 500 subjects, the oil was washed off after 5 minutes. The results are summarized in the following table. Reaction None Mild Strong Column Total Within 5 Minutes After 5 Minutes 391 65 44 500 66 341 93 500 Row Total 457 406 137 1000 Let's use the following notation for the various events: W= washing oil off within 5 minutes, A = washing oil off after 5 minutes, N = no reaction, M = mild reaction, S = strong reaction. Find the following probabilities for a person selected at random from this sample of 1000 subjects. (Use 3 decimal places.)

(42)  Matt has three times as many stickers as David. How many stickers must Matt give David so that they will each have 100 ​stickers? Check that your answer is correct.