Probability States - Mastering AMC 10/12

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In this video, we will cover Probability States, also known as Markov Chains. We will convert conceptually tricky probability problems into simple equations using states.
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For more practice, watch the AMC 10/12 Fundamentals Classes here:

If you need a refresher on the fundamentals, check out:
1. AMC 8 Fundamentals:

2. AMC 8 Advanced:

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Tags:
AMC 10, AMC10, AMC 12, AMC12, AMC 10 Preparation, AMC 10 Crash Course, AMC 10 Concepts, AMC 12 Preparation, AMC 12 Crash Course, AMC 12 Concepts, AMC 10 Review, AMC 12 Review, Number Theory, Primes, Factors Competition math, number of factors, sum of factors, product of factors, AMC 10 number theory, AMC 12 number theory, diophantine equations, divisibility competition math, Area of a Triangle, Similar Triangles, Cyclic Quadrilateral, Power of a point, 3D Geo, Polygons, Coordinate Geometry, Trigonometry, Logarithms, Complex Numbers, Inequalities, Floor and Ceiling Functions, Generating Functions

[menderelcapbig]

I came here because of the last straw of taking like 8 minutes on the frog problem. These are much better methods than brute force. Thank you so much!!

[theevilmathematician]

For the first problem notice that there is a (1/2)^3 = 1/8 chance of same flip. So it is a geometric series, which can be trivially found as 1/7, B.

[theevilmathematician]

2nd problem is also casework to get 25/32

[AmanKamath-jcvz]

For question 3 how is there a 1/4 chance for P(111) because there is a 1/2 chance that each of the 3 will give their dollar to the person on the right or left. If 2 people give their dollar to the person on the right that does not guarantee that the 3rd person will do the same. If three people give it to the right with 1/2 chance of that then it would be a 1/6 chance of it being P(111)n after P(111)n-1. Can you tell me how I am wrong?

[PioneersOppenheimer]

What grade are you in, because I am a 9 th grader and I think that I am pretty late to start studying for it.

[names]

Hi bro do you have a discord or tele server?