Evaluation of Mathematics for grade XI ( SMA 1 Blitar )

This evaluation is purposed for grade XI ( IA5 and IA 6 and also IA 8 + IA 1)
Solve the following correctly, send your answers by mail into endrayanaputut29@gmail.com before monday, 15th Nov,2010

1. A bag contains ten counters, of which six are red and four are green. A counter
is chosen at random, its colour is noted and it is replaced in the bag. A second
counter is then chosen at random. Find the probabilities that :
a. both counters are red
b. both counters are green
c. just one counter is red
d. at least one counter is red
e. the second counter is red

2. Events A, B, and C satisfy these conditions:
P(A) = 0.6; P(B) = 0.8; P(B|A) = 0.45; P(B and C) = 0.28
Calculate :
a. P(A and B)
b. P(C|B)
c. P(A|B)

3. Calculate the number of arrangements of the letter in the word NUMBER. How many
arrangements if at begin and end is a vowel ?

4. a. Given that 5 sin X + 12 cos X = R sin ( X + Y), find the values of X and Y
for which R > 0 and 0 b. Find all values of X between 0 and 360 satisfying :
(i) 5 sin X + 12 cos X = 4
(ii) 5 sin 2X + 12 cos 2X = 13 sin X
c. Find the greatest and smallest positive value of X at which this occurs:
12 cos X + 5 sin X + 20

References : Statistics 1 and Graded Exercises of Pure Mathematics