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- ange of Pla x C ■ Bb Probability que X Bb Statistics and p X X learn-eu-central-1-prod-fleet01-xythos.content.blackboardcdn.com/60d4531e78936/3438094?X-Blackboard-S3-Bucket-learn-eu-central-1-prod-fle... Probability question sheet N Netflix Esc FnLock b) less than three are damaged. a) all 15 will pass b) none will pass and c) at least 12 will pass. A Z -- Q I 0. The probability of passing an exam is 0.7. Out of 15 students, evaluate the probabilities that Type here to search F1 11. Determine the probabilities of having (a) at least 1 girl and (b) at least 1 girl and 1 boy in 23:12 23/04/2023 Alt 11 X 2 S W X AI F2 Vectors.pdf www 3 43 ww A+ F3 E с F4 4 et V 0 - F5 2/4 | % 5 G 0+ F6 B - Y H & 7 N 200% + @ F8 U J 00* 8 Bb Probability que X W F9 M K * F10 61 ( 9 Alt Gr L 6°C O Δ· F12 2 Probability PX + P 117 PrtSc Home [ 6 Ctrl End +11 } J ENG Insert ( # + PgUp K Delete5. A candy dish contains 2 red (R) and 4 yellow (Y) candies. You close your eyes, select two candies from the dish (without replacement), and record their colors. Use general multiplication rule and special addition rule to find the following probabilities. a. The probability that the first selected candy will be red and the second selected candy will be yellow is b. The probability that two selected candies will be of different colors_ One is red, another one is yellow c. Probability that two selected candies will be of the same color_ Both are red or both are yellow Assuming that the event "The first selected candy will be red and the second selected candy will be yellow "is denoted by A, the event "Two selected candies will be of different colors" is denoted by B, and the event "Two selected candies will be of the same color" is denoted by C, show your work in finding P(A), P(B), and P(C) in the questions a, b, and c.I was wondering if you could help me understand how to find the probability of failure of the entire deck system assuming that the failures of groups A, B and C are independent of each other and that the failures of sub-groups B1 and B2 are also independent of each other
- Suppose there are a million cars made by a car company across the globe, where the probability that a car has a defective brake part is 0.0002. Based on the Monte Carlo algorithm, determine the minimum number of cars that needs to be tested so the probability of finding not even a defective car among those tested is less than two in a million. Use a calculator to simplify your answer and obtain the minimum number of cars.Look at the 4 probability rules beow , an provide a REAL LIFE example for each. Also, with a Real LIfe EXAMPLE, explain how Disjoint events CAN be dependent. Rule 1. The probability P(A) of any event A satisfies 0 ≤ P(A) ≤ 1. Rule 2. If S is the sample space in a probability model, then P(S) = 1. Rule 3. Two events A and B are disjoint if they have no outcomes in common and so can never occur together. If A and B are disjoint, P(A or B) = P(A) + P(B) This is the addition rule for disjoint events. Rule 4. For any event A, P(A does not occur) = 1 − P(A)A cybercafe buys 45% of its laptop from Company A, 35% from Company B and 20% from Company C. However, 20% of laptop from Company A is prone to defect whereas 10% from Company Band 5% from Company C. Draw a tree diagram for the situation and hence find the probability the laptop is from Company Cif it is defect.
- Each of two parents have the genotype red/blonde, which consist of the pair of alleles that determin hair color, and each parent contributes one of thoes alleles to a child. Assume that if the child has atleast one re allele, that color will dominate and the childs hair color will be red. List diffrent out comes, Assume these outcomes are equal likley probability of a child of these parents will have the blonde/blonde genotype? What is the probability that the child will have red colored hair ?An urn has 20 black and 20 white balls. We randomly remove balls, one at a time until the balls in the bag have the same colors to each other (or there is only 1 ball left in the bag). Please calculate the expectation of the number of balls left in the bag eventually. Find your numerical answer with error less than 1. (Calculator is allowed).8. The NACHR ion channel can be in one of three states: resting (R), closed with Ach bound (C), and open (0) with transition probabilities (per one microsecond): 0.04 (from R to C), 0.07 (from C to R), 0.12 (from C to O) and 0.02 (from O to C); the other transition probabilities are 0. Suppose that initially 3/4 of ion channels are in R and 1/4 are in C. What fraction of the ion channels is open after 1 microsecond? After 2 microseconds? 9. There are three kinds of vegetation in an ecosystem: grass, shrubs, and trees. Every year, 25% of grassland plots are converted to shrubs, 20% of shrub plots are converted to trees, 8% of trees are converted to shrubs, and 1% of trees are converted to grass; the other transition probabilities are 0. Suppose that initially the ecosystem is evenly split: 1/3 grass, 1/3 shrubs and 1/3 trees. What fraction of ecosystem is covered in shrubs after 1 year? after 2 years?
- please be clearA service company receives on average 4 service requests per day. The requests are received randomly according to Poisson process. The company has 2 service engineers and sends one engineer to attend each request. 1 An engineer needs an exponentially distributed service time with the mean of day(s). 2 The company's policy is to have maximum of 2 requests waiting in the queue If this number is reached, all incoming requests are rejected (sent to a competitor). Answer the following questions based on the information provide above: (a) Using the Kendall's notation, indicate what type of queueing system it is: (b) Compute the system state probabilities (provide at least 3 decimals): Po = P1= P2 = P3 = Pa = (c) Compute the expected total number of customer requests (waiting and served) in the system. ELL] = (d) Compute the expected number of accepted requests. Aaccepted = (e) Compute the expected total processing time (waiting + being served) for the accepted requests. E[Time] =