11 Probability of an Event
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The definition of probability of an event is explored here as a part of the axiomatic approach to probability. We also take a look at probability of equally likely events occurring.
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Lam's Theorem states that the number of steps (n) required to compute the greatest common divisor (GCD) of two numbers (x and y) using Euclid's algorithm is bounded above by the logarithm of x/φ, where φ is the golden ratio. The maximum value of n occurs when x and y are consecutive Fibonacci numbers. The theorem draws on over 5000 years of mathematical history, from the ancient Egyptians' use of the golden ratio to Euclid's algorithm from 300 BC to Gabriel Lamé's theorem in 1845.
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11 Probability of an Event
- 1. Maths topic for Probability: probability of an event By Dhruv Sethi; dhrsethi1@gmail.com/+91 9310805977 11th Grade
- 2. Probability of an Event Let a sample space of an experiment be S = {w1, w2, w3, …, wn} Let all the outcomes be equally likely to occur i.e. the chance of occurrence of each simple event must be the same. Σ P(wi) = p for all wi ∈ S where 0 ≤ P(wi) ≤ 1 since Σ P(wi) = p + p +…(n times) … + p = 1 np = 1 i.e. p = 1/n
- 3. Probability of an Event Also, let S be a sample space and E be an event, such that n(S) = n and n(E)=m. If each outcome is equally likely, then it follows that P(E) = m/n = (Number of outcomes favourable to E)/(Total possible outcomes)
- 4. Probability of an Event • You can contact me for private or group tuitions from the details below • By Dhruv Sethi: +91 9310805977/dhrsethi1@gmail.com • Whatsapp: +91 8291687783