From the tree diagram find the following. (a) P(A n E) (b) Р(А) (c) P(AIE) А 0.2 0.4 0.2 0.4 C А 0.1 0.8 0.2 В 0.7
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- Information theory is concerned with the transmission of data, usually encoded as a stream of 0s and 1s, over communication channels. Because channels are “noisy,” there is a chance that some 0s sent through the channel are mistakenly received at the other end as 1s, and vice versa. The majority of digits sent, however, are not altered by the channel. Draw a tree diagram that depicts the type of bit sent (either 0 or 1) and the type of bit received at the end of the channel.Suppose there are 14 boys and 6 girls in a classroom. A teacher randomly selects 5 students from the class without replacement. What is the probably that the selected students contain 3 girls?Suppose we select 2 students randomly from a class of 20 students. The first student selected will analyze a data set on the computer and prepare summary tables, and the second student will present the results to the class. How many ways can the students be selected for these tasks? Is this a permutation, a combination, or neither?
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- In a survey of 30 students on a class it is seen that, 19 students math, 17 students music 11 students history, 7 students math and history, 12 students math and music 5 students music and history and 2 of them are studing taking above three subjects. From the above data show that (1) How many students are studing taking math but avoiding history? (2)How many of them studying absolutely taking two subjects?On August 31 there are five wild-card terms in theAmerican League that can make it to the play-offs, andonly two will win spots. Draw a tree diagram which showsthe various possible play-off wild-card teams.Suppose there are 14 men and 6 women in an office. A CEO randomly selects 5 workers from the office without replacement. What is the probably that the selected workers contain 3 women?
- An analysis of first-year students at a college revealed that 1/4 of the first-year women were from homes where both parents were professionals. Of these, 3/5 were interested in the same profession as one or both of their parents. If this latter group is made up of 21 students, how many first-year women are there?How many ways can we choose 3 items at random without replacement from 5 items if the order of the selected items is not important?Suppose five different engineering trails, i.e., Machine Learning, Power Engineering, Optics and Photonics, Microwave Communication, and Biomedical Engineering have been offered at University of Cambridge in Spring 2020, where each of the trail has exactly 12 courses. If the individual course and the order in which the courses are selected does not matter, then how many ways are there for an undergraduate student to select randomly 6 courses from these five different trails in that semester. Show your work and calculation with relevant explanation in detail.
