# Probability Problem Solving

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Try it risk-free Colin is starting his own business.

He wants to sell ties that look like different objects.

I have also written several books about mathematical puzzles, paradoxes, and related topics available on Amazon.

Sources Adapted from Twitter/Math Stack Exchange https://twitter.com/Mj Eff Ger Aso N/status/1122173214854135808 https://math.stackexchange.com/questions/3103891/gcse-probability-question-relating-to-trees-help-please I am the author of The Joy of Game Theory: An Introduction to Strategic Thinking.

Favorable cases = (1, 6) (6, 1) (2, 5) (5, 2) (3, 4) (4, 3) --- 6 ways. Sol: (i) honor cards = (A, J, Q, K) 4 cards from each suits = 4 × 4 = 16 P (honor card) = 16/52 = 4/13 (ii) face cards = (J, Q, K) 3 cards from each suit = 3 × 4 = 12 Cards. So there are total 7 cases out of which (Sat, Sun) (Sun, Mon) are two favorable cases. of ways in which two particular people sit together is 13! The probability of two particular persons sitting together 13! 1 of the bags is selected at random and a ball is drawn from it.

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. A problem like this can be intimidating because it contains a lot of details. The GCSE exam always has great probability questions like this one.As a member, you'll also get unlimited access to over 79,000 lessons in math, English, science, history, and more.Plus, get practice tests, quizzes, and personalized coaching to help you succeed. Answer To Tricky GCSE Probability Problem(Pretty much all posts are transcribed quickly after I make the videos for them–please let me know if there are any typos/errors and I will correct them, thanks).(rated 4.1/5 stars on 7 reviews) 40 Paradoxes in Logic, Probability, and Game Theory contains thought-provoking and counter-intuitive results.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.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.Related Topics: Introduction To Probability Probability Tree Diagrams Theoretical vs.Experimental Probability In these lessons, we will learn how to solve some probability word problems.

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