1. Y Dosraniad Binomial Profion Bernoulli - Bernoulli Trials Profion sydd â dim ond 2 ganlyniad posibl. A Bernoulli trial is a random experiment with only 2 possible outcomes. e.e. taflu ceiniog, e.g. tossing a coin, cael y rhif 6 wrth daflu dîs. throw a 6 when a die is thrown. Cyfeirir at y canlyniadau yma fel ‘llwyddiant’ a ‘methiant’ a gelwir y dosraniad tebygolrwydd ar gyfer y math yma o brofion yn Ddosraniad Binomial (Dosraniad Binomaidd) The Binomial Distribution The outcomes of these trials are called ‘success’ and ‘failure’ and the probability distribution for these trials is called the Binomial Distribution.

2. Os oes gan X ddosraniad binomial, rydym yn ysgrifennu If X has a binomial distribution, we write X ~ B ( n, p ) n = nifer y treialon p = tebygolrwydd o lwyddiant P(X = x) q = tebygolrwydd o fethiant (q = 1 – p) n = number of trials p = probability of success q = probability of failure (q = 1 – p)

3. Enghraifft - Example Teflir dîs 8 gwaith. Cyfrifwch y tebygolrwydd y ceir sgôr o 6 A die is thrown 8 times. Calculate the probability that a score of 6 is obtained a)union 3 gwaith, exactly 3 times, b)o leiaf 7 gwaith, at least 7 times, c)o leiaf 2 waith. at least twice. X ~ B ( 8, ) a) P(X = 3) = 56 x 0.0046 x 0.40188= 0.1042

4. b) P(X ≥ 7)= P(X = 7) + P(X = 8) = 0.0000238 + 0.000000595 = 0.00002441 c) P(X ≥ 2)= 1 – P(X < 2) = 1 – [P(X = 0) + P(X = 1)] = 1-(0.232568 + 0.37210886) = 0.395323

5. Ymarfer/Exercise 4.5a Mathemateg - Ystadegaeth Uned S1 – CBAC Mathematics Statistics Unit S1 - WJEC