The random variable X X\,X has the distribution X∼B(6,0.35)X\sim B(6,0.35)X∼B(6,0.35).
One term in the expansion of (0.65+0.35)6(0.65+0.35)^6(0.65+0.35)6 is (62)(0.65)4(0.35)2\binom62(0.65)^4(0.35)^2(26)(0.65)4(0.35)2.
State the probability involving X X\,X that this term represents.
Explain why the sum of all seven terms in the expansion is equal to the sum of the probabilities P(X=r)P(X=r)P(X=r) for r=0,1,…,6r=0,1,\ldots,6r=0,1,…,6.
390 exam-style questions on OCR A Level Maths 2.4 Statistical Distributions, covering 2.4.1 Discrete probability distributions, 2.4.2 Binomial distribution as a model, 2.4.3 Calculating binomial probabilities, 2.4.4 Mean and variance of the binomial (A-level only), 2.4.5 Normal distribution as a model (A-level only), 2.4.6 Probabilities using the normal distribution (A-level only), 2.4.7 Links to histograms, mean and standard deviation (A-level only), and 2.4.8 Selecting an appropriate distribution (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.