# Solved Problem

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.

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