STARTER The probability that a particular page in a maths book has a misprint is 0.2. Find the probability that of 12 pages in the book: 4 of them have.

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Presentation transcript:

STARTER The probability that a particular page in a maths book has a misprint is 0.2. Find the probability that of 12 pages in the book: 4 of them have a misprint n = 12 and p = 0.2 P(X = 4) = 0.133 Fewer than 2 of them contain a misprint. P(X < 2) = 0.0687 + 0.2062 = 0.275

STARTER If X ≈ B (n, 0.6) and P (X< 1) = 0.0256, find n Therefore P(X = 0) = 0.0256 0.0256 = nC0 (0.6)0 (0.4)n = 1 x 1 x (0.4)n 0.4n = 0.0256 n = 4 (Solver or by taking logs each side)

Note 5: Expected Value of a Binomial Distribution For the binomial distribution where the expectation of X (or mean of X) is E(X) = np

Example: A farmer plants 150 gum trees, each of which have an individual probability of surviving the winter conditions of 0.8. Find the expected number that survive the winter. E(X) = np = 150 × 0.8 = 120

New Book Page 535 Exercise 15E and F