4. What is the probability distribution if X ~ B(3,0.82)? О Р(Х — 0) — 0.55 P(X = 1) = 0.36 Р(X — 2) — 0.08 P(X = 3) = 0.01 P(X = 0) = 0.03 P(X = 1) = 0.21 P(X = 2) = 0.37 P(X = 3) = 0.61 О Р(Х — 0) — 0.01 Р(Х — 1) — 0.08 Р(Х %3D 2) — 0.36 P(X = 3) = 0.55 P(X = 0) = 0.11 P(X = 1) = 0.20 Р(X — 2) — 0.26 Р(X — 3) — 0.43 %3D %3D

f the probability of a new employee in a​ fast-food chain still being with the company at the end of the year is 0.7​, what is the probability that out of 8 newly hired people   ​(A) 5 will still be with the company after 1​ year? ​(B) 5 or more will still be with the company after 1​ year?   Round each of the calculations to three decimal places when going through the solution process.

A particle executes an unrestricted simple random walk on the line with p=0.7 and q=0.3. Its position at time n is represented by the random variable Xn, n = 0, 1,...; Xo = 0. (a) Calculate the values of the following probabilities. (i) P(X5 = -2) (ii) P(X6 = 2) (b) Calculate the probability that the particle returns to its starting point for the first time after 8 steps. (c) After the particle has been moving for some time, it is observed to be located at the point +3. (i) Calculate the probability that the particle will ever return to the origin from the point +3. (ii) Calculate the probability that starting from the point +3, the particle will visit the point +8 without first visiting the origin.

Medical researchers developed a test that determines whether a person has a particular disease. The results have produced the following probabilities, where D represents having the disease and N represents a negative test. P(D'IN) = 0.85 and P(DIN') = 0.72. Assuming that P(N") = 0.12, find P(N'|D). P(N'|D) =O (Round to the nearest thousandth as needed.)