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
P(X < 1) = 0.0256
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