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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.

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So he began working on a solution three years ago, and eventually invited González-Acuña to solve it with him. “The second surface is such that it corrects all the aberration generated by the first surface, and the spherical aberration is eliminated.”Head spinning aside, González-Acuña's formula has serious real-world potential.

“I remember one morning I was making myself a slice of bread with Nutella, when suddenly, I said out loud: Mothers! Beyond consumer needs, it could make for sharper lenses on scientific and medical equipment, from telescopes to microscopes.

“Angular Dependence for ν‘, j’-Resolved States in F H2 → HF(ν‘, j’) H Reactive Scattering Using a New Atomic Fluorine Beam Source” I can see if he wants to weigh in… please do Trevor: PEMDAS Andrew: i'll also fire off the request to my go-to physicist who also just answered the POP question of how to jump from a moving train Taylor: tbh it would be awesome if we could find experts who disagree Trevor: wait revisited my interpretation of PEMDAS back to 16this is why I went to art school Taylor: I asked my friend [REDACTED], who is about to graduate with her phd in statistics from [REDACTED] and has three or four math masters degreesand i am so pleased to report she's on my side Derek: [REDACTED] wins Andrew: but what did [REDACTED] say was the answer??!

Taylor: there is no answer, fake question designed to stoke outrage Bill: maybe our smart take is: math is not subjective, nobody writes math like this, here is what's wrong Taylor: she's just getting started Kit: Sounds like [REDACTED] needs to write the sweaty math take Andrew: daaaaang [REDACTED]go off Bobby: no we're onto something! D., Associate Professor of Physics at Southeastern Louisiana University, Who Delivered the Final Verdict and Decisively Shut Us All Up Of course this isn't math. We have conventions on how to write these things just like we have conventions on how to spell stuff. Some people spell it as ‘gray’ and others as ‘grey.’ We still understand what's going on.

Sol: Sample space = [HHH, HHT, HTH, THH, TTH, THT, HTT, TTT] Total number of ways = 2 × 2 × 2 = 8. Cases = 7 P (A) = 7/8 OR P (of getting at least one head) = 1 – P (no head)⇒ 1 – (1/8) = 7/8Example 2: Find the probability of getting a numbered card when a card is drawn from the pack of 52 cards. Numbered Cards = (2, 3, 4, 5, 6, 7, 8, 9, 10) 9 from each suit 4 × 9 = 36 P (E) = 36/52 = 9/13Example 3: There are 5 green 7 red balls. P (getting a sum of 22 or more) = 15/1296 = 5/432 = 36 Since the number on a die should be multiple of the other, the possibilities are (1, 1) (2, 2) (3, 3) ------ (6, 6) --- 6 ways (2, 1) (1, 2) (1, 4) (4, 1) (1, 3) (3, 1) (1, 5) (5, 1) (6, 1) (1, 6) --- 10 ways (2, 4) (4, 2) (2, 6) (6, 2) (3, 6) (6, 3) -- 6 ways Favorable cases are = 6 10 6 = 22.

Two balls are selected one by one without replacement. So, P (A) = 22/36 = 11/18Example 13: Find the probability that a leap year has 52 Sundays.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?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.Every few months, the Internet eats itself over some kind of viral riddle or illusion, each more infuriating than the last.And so, like clockwork, this maddening math problem has gone viral, following in the grand tradition of such traumatic events as The Dress and Yanny/Laurel.Here’s a heated chat between the editors who stopped doing any semblance of actual work for the day to solve an equation designed to flummox fourth graders—and make many enemies in the process—followed by insight from real mathematicians and physicists who begrudgingly responded to our request for comment to solve the enraging math debate, once and for all. What if you want to do it the long way and use the distributive property and distribute the 2 first? Or does the distributive property suddenly no longer apply? Derek: I trust Morgan because she's had a math class this decade. Dan: smart Berkley people say it's too ambiguous to say; PEMDAS isn't a mathematical convention as much as a teaching method Pat: multiplication/division::right/wrong Taylor Rojek, associate features editor: Biggest takeaway isn't that anyone sucks at doing math, but that this person sucks at writing out clear equations Bill Strickland, editorial director: MAKE IT CONTENT! Pat: The equation is not written according to ISO standards, leaving ambiguity of interpretation and the real answer is we need to teach better math writing.Pat: Wikipedia says you hate America if you get 16. Ambiguous PEMDASAmbiguous problems, order of operations, PEMDAS, BEMDAS, BEDMASaka..Taylor said, but from Harvard Morgan: aka...teach the distributive property instead of random acronyms Pat: When written according to ISO standard, the answer is 1.Since Diocles brought up the problem, nobody in history has been able to find a good answer.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.

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