If two events A and B, are such that P (A) = 0.4, P(B) = 0.3, and P(A Intersecti
ID: 3230874 • Letter: I
Question
If two events A and B, are such that P (A) = 0.4, P(B) = 0.3, and P(A Intersection B) = 0.1, then (1) P(A|A Union B) = (a) 2/3, (b) 1/2, (c) 1/6, (d) 1. (2) P(A|A Intersection B) = (a) 2/3, (b) 1/2, (c) 1/6, (d) 1. (3) P(A Intersection B) = (a) 2/3, (b) 1/2, (c) 1/6, (d) 1. A random variable Y has a distribution f (y) = (1/5)e^-y/5 for y > 0 or 0 elsewhere. Then P(Y > 6|Y > 2) = (a) P(Y > 1), (b) P(Y > 2), (c) P(Y > 3), (d) P(Y > 4). Males and females react differently to a circumstance. It is observed that 80% of the females react positively to the circumstance, whereas only 40% of males react positively. A group of 20 people, 15 female and 5 male, was subject to these circumstances. A response picked at random from the 20 was negative. The probability that is was that of a male is: (a) 1/3, (b) 1/2, (c) 1/6, (d) 2/5. A multiple-choice question has four possible answers. The probability a student knows the answer is 3/4 and the student will guess is 1/4. The probability of guessing a correct answer is 1/4. If the student correctly answers a question, the probability that the student really knows the correct answer is: (a) 1, (b) 36/37, (c) 16/17, (d) 12/13. Explosive devices in mining operations produce nearly circular craters when detonated. The radii of these craters are exponentially distributed with mean 5 feet. The mean of the areas produced by these devices is: (a) 50 pi, (b) 100 pi, (c) 200 pi, (d) 400 pi.Explanation / Answer
P(A only) = P(A)-P(A intersection B) = 0.4-0.1-0.3
P(B only) = P(B) - P(A intersection B) = 0.3-0.1=0.2
P( P(A intersection B)) = 0.1
1)P(A/AUB) = 0.4/[0.3+0.2+0.1]=2/3
2) P (A/AintersectonB) = 1
3) P(A intersection B/ A U B) = 0.1/0.6=1/6
Please repost the rest individually.