What is the probability that the ball be black? If a person

grabbed a black ball. What is the probability that the ball came from urn B?

6. The probability of catching Lyme disease after on day of hiking in the Cuyamaca mountains are estimated at less than 1 in 10000. You feel bad after a

day of hike in the Cuyamacas and decide to take a Lyme disease test. The

test is positive. The test specifications say that in an experiment with 1000

patients with Lyme disease, 990 tested positive. Moreover. When the same

test was performed with 1000 patients without Lyme disease, 200 tested

positive. What are the chances that you got Lyme disease.

7. This problem uses Bayes' theorem to combine probabilities as subjective

beliefs with probabilities as relative frequencies. A friend of yours believes

she has a 50% chance of being pregnant. She decides to take a pregnancy

test and the test is positive. You read in the test instructions that out of

100 non-pregnant women, 20% give false positives. Moreover, out of 100

pregnant women 10% give false negatives. Help your friend upgrade her

beliefs.

8. In a communication channel a zero or a one is transmitted. The probability

that a zero is transmitted is 0.1. Due to noise in the channel, a zero can be

received as one with probability 0.01, and a one can be received as a zero

with probability 0.05. If you receive a zero, what is the probability that a

zero was transmitted? If you receive a one what is the probability that a one

was transmitted?

9. Consider a probability space (?, F, P). Let A and B be sets of F, i.e., both

A and B are sets whose elements belong to ?. Define the set operator $$

EIN-3235 HW-04 FIL Problem No. 4.4 / 10 pas. Let S be the event that a randomly selected FIU student has taken a "Statistics" course. Let C be the event that the same student has taken a "Circuit Analysis" course. Suppose P(S) = 0.39, P(C) = 0.31, P(SC) = 0.22 1) Find the probability that a student has taken Statistics, Circuit Analysis, or both. 2) Find the probability that a student has taken neither Statistics nor Circuit Analysis. 3) Find the probability that a student has taken Statistics, but not Circuit Analysis. Show your explanations. Displaying only the final answer is not enough to get credit. Solution (Show all intermediate steps, formulas, calculations, explanations and comments below this line. Don't write above this line)Probability & Statistics 1. The number of named tropical storms per year is distributed Poisson with X = 10 a. (5 points) What is the average number of named tropical storms? b. (5 points) What is the probability there will be fewer than 5 named tropical storms in a randomly selected year? Show your calculations.according to the "Koch" poll roughly 93% of students like to take Statistics!! If 8 students are polled find the following (round answers to 6 decimal places if needed): (p.s. the graph in the back will not help you ) a) Find the probability exactly 6 students like statistics. b) Find the probability more than 6 students like statistics. c) Find the probability no more than 2 students like statistics. d) Find the probability at least one student likes statistics