# Solved Problem No matter how high-quality the camera, math has dictated that the curve of optical lenses would always be slightly softer than the center. González-Acuña, a doctoral student at Mexico’s Tecnológico de Monterrey, up and solved it.

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And considering the massive uptick in camera ownership over the last two decades, that's saying something. Chaparro-Romo, a doctoral student at the National Autonomous University of Mexico (UNAM), had a feeling that the problem could be solved. By using an extremely complex mathematical formula, published in an article titled "General Formula for Bi-Aspheric Singlet Lens Design Free of Spherical Aberration," in the journal Yeah.“In this equation we describe how the shape of the second aspherical surface of the given lens should be given a first surface, which is provided by the user, as well as the object-image distance,” González-Acuña tells Peta Pixel.What is the probability that the problem is solved? E1 = First bag is chosen E2 = Second bag is chosen E3 = Third bag is chosen A = Ball drawn is red Since there are three bags and one of the bags is chosen at random, so P (E1) = P(E2) = P(E3) = 1 / 3 If E1 has already occurred, then first bag has been chosen which contains 3 red and 7 black balls.Sol: Probability of the problem getting solved = 1 – (Probability of none of them solving the problem) = 1296. The probability of drawing 1 red ball from it is 3/10.Find the probability that first is green and second is red. Sol: A leap year can have 52 Sundays or 53 Sundays.Sol: P (G) × P (R) = (5/12) x (7/11) = 35/132Example 4: What is the probability of getting a sum of 7 when two dice are thrown? In a leap year, there are 366 days out of which there are 52 complete weeks & remaining 2 days.P (A) = 6/36 = 1/6Example 5: 1 card is drawn at random from the pack of 52 cards. P (face Card) = 12/52 = 3/13Example 7: Three dice are rolled together. So, P (53 Sundays) = 2 / 7 Now, P(52 Sundays) P(53 Sundays) = 1 So, P (52 Sundays) = 1 - P(53 Sundays) = 1 – (2/7) = (5/7)Example 14: Fifteen people sit around a circular table. If the ball drawn is red, find the probability that it is drawn from the third bag.What is the probability as getting at least one '4'? Probability of getting number ‘4’ at least one time = 1 – (Probability of getting no number 4) = 1 – (5/6) x (5/6) x (5/6) = 91/216Example 8: A problem is given to three persons P, Q, R whose respective chances of solving it are 2/7, 4/7, 4/9 respectively. What are odds against two particular people sitting together? Sol: Let E1, E2, E3 and A are the events defined as follows.I have my own flow, sound and bars and my lyrics has a meaning, peace!Example 1: A coin is thrown 3 times is the probability that atleast one head is obtained?These kinds of conundrums are purposely meant to divide and conquer, and predictably, the seemingly simple problem posed in the offending tweet—8÷2(2 2)—practically caused a civil war in the magazines. Bobby Lea, test editor (and three-time Olympic cyclist): i ride bikes Matt Allyn, features director: for anyone that wants a longer explanation of why you divide before multiply in this case Pat Heine, video producer: ..writes out PEMDAS and then does PEDMASMatt: you clearly didn't listen Pat: i didn't...i was busy correcting her math. Matt: ok, Derek, the video's for you Pat: if you get 16 it's because you don't know the difference between brackets and parentheses.Naturally, we took to Slack to hash out our differences. Morgan Petruny, test editor: I agree with Derek and disagree with You Tube. Bobby: This sounds like a conversation the belongs on the Not My Job segment of Katie Fogel, social media editor: polling our IG audience on this now...

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