Professor Nowotny likes to cook. He cuts his potatoes into thin slices and fries them in a pan. He puts them in and occasionally tosses them. At each toss the potato slices fall independently of each other with pr the same side and probability 1-p onto the other side. Q1: For n slices, what is the probability that they all fall back onto the same side in a single toss? A p" B1-p" C n p Dn (1-p) E (1-P)" [Select] Q2: He has n slices and tosses k times. What is the probability that all slices have both sides fried, i.e. have fallen at least once on the other side? Ak-p" Bn p C (1-p") D (1-pk)n E (1-p)nk [Select] v Q3: Professor Nowotny has n slices in the pan and would like to have them all fried on both sides with probability >99%. How many times k does he need to toss at least? log(0.01) Ek D KZ log(P) log (1-(0.01)") log(p) C kz log(1-(0.99)/") log(p) log((0.99)¹/) log(p) A k2 [Select] V B k> log(1-(0.99)¹/") log(1-p)

Solve.

Susie has three children. Josh has a z-score of 0.87 for his height and David has a z-score of 0.13 for his height. Solve for the probability the Kelley will have a height between her brothers. Positive z-scores: Z 0.0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.0 0.5000 0.5040 0 5080 0 5120 0.5160 0.5199 0.5239 0.5279 0.1 0.5398 0.5438 0.5478 05517 0.5557 0.5596 0.5636 0.5675 0.2 0.5793 0.5832 0.5871 0 5910 0.5948 0.5987 0.6026 0.6064 03 06179 0 6217 0.6255 0. 6293 0.6331 0.6368 0.6406 0. 6443 0.4 0 6554 0.6591 0.6628 0.6664 0.6700 0 6736 0.6772 0.6808 0.5 0.6915 0.695o 0.6985 07019 0.70540.7088 0.7123 07157 0.6 0.7257 0.7291 0.7324 0.7357 0.7389 0.7422 0.7454 0.7486 DELL %24 & 23 8) 4 7 の 10

tab Carlos buys a bax of doughnuts. The box contains 9 chocolate glazed, 5 Boston crème, and 7 powdered sugar doughnuts. He reaches into the box and randomly selects a doughnut, then reaches into the box again and selects another doughnut. What is the probability that he randomly selects a Boston crème first and then a chocolate glazed doughnut? Round your answer to three decimal places. esc ps lock ! 1 Q F1 A 2 F2 W S #3 80 F3 E D $ 4 Q F4 R F % 5 0 F5 T : ^ 6 G G F6 Y C & 7 H ‹k F7 U * 00 8 N F8 ( 1 DD 9 F9 JK M ) 0- O 72 F10 < 4 P F11 ^ + F12 = [ 11 S I

Grades earned in a class are recorded for 2 group of students (students taking only History and the others only taking Biology), the grades in those classes are summarized below. A B C History 19 9 20 Biology 7 2 10 Total 26 11 30 Total 48 19 67 If one student was chosen at random, find the probability that the student got a B. Give your answer as a fraction or decimal.

A and B part

Q11 At a soccer (aka football) game, the probability of a goal keeper saving from a penalty kick is 0.3. After facing five different penalty kicks, assuming each penalty kick is independent, what is the probability that the goal keeper saves exactly three of the penalty kicks?

Solve it fast and correctly. I will rate accordingly with multiple votes. Need 100% correct answer. There are eight seats at a rectangular table - three on each of the longer sides and one on each of the shorter sides. Six adults and two children sit around the table, with each seating configuration equally likely. What is the probability that the two children will end up seating next to each other on one of the longer sides of the table?

Charlie is about to take two laps in the school swimming pool. The time of his first lap is X minutes,  where X is an Exponential(1) random variable. The time of his second lap is Y minutes, where Y is an Exponential(X) random variable. What is the probability that he completes his second lap within one minute?