Exercises
11-1. A box contains 10 white balls, 3 black balls and 2 red balls.
(a) What is the probability of drawing a white ball?
(b) What is the probability of drawing a black ball?
(c) What is the probability of drawing a red ball?
11-2. A box contains 10 white balls, 3 black balls and 2 red balls.
(a) What is the probability of drawing a white ball and then drawing a black ball?
(b) What is the probability of drawing two white balls?
(c) What is the probability of drawing a red ball and then a black ball?
11-3. A bowl of fruit contains 3 apples, 5 oranges and 3 pears. If two fruits are
selected at random,
(a) What is the probability of getting 2 pears?
(b) What is the probability of getting 2 apples?
(c) What is the probability of getting 2 oranges?
11-4. Calculate the mean, variance and standard deviations of the following.
(a) G=grade of student on 6 exams. G={ 84 , 91 , 72 , 68 , 87 , 78 }
(b) T=test scores for class of 17 students.
T={ 71 , 82 , 66 , 88 , 100 , 97 , 96 , 100 , 77 , 77 , 84 , 89 , 93 , 98 , 100 , 100 , 75 }
(c) A= Average absenteeism rate in days missed per 100 working days over 6 year
period taken from a certain factory. A={ 8. 05 , 13. 35 , 5. 10 , 4. 43 , 6. 22 , 7. 81 }
11-5. Show that s^2 =
1
n− 1
∑m
j=1
(xj−x ̄)^2 nf jcan be written
s^2 =^1
n− 1
∑m
j=1
x^2 jnfj−^1
n
∑m
j=1
xjnf j
2
11-6. If a pair of fair dice are rolled and Xdenote the sum of the upward numbers,
then find the probabilities of rolling a 2,3,4,5,6,7,8,9,10,11 and 12.
