Maths(四)---Probability and Statistics(4)

Complementary Events

例一.
A sequence of 8 bits is randomly generated. What is the probability that at least one of these bits is 1?

Solution
Hence, the probability that the bit string will contain at least one 1 bit is 255/256 .

The Probability of Union
例一.
In a class of 40 students, 6 out of 15 boys and 13 out of 25 girls wear glass. Whatis the probability that a student chosen at random from the class is a boy or someonewho wears glasses?

Solution
15/40+19/40-6/40=28/40=7/40

例二.
What is the probability that a positive integer selected at random from the set of positive integers from 1 to 60 inclusive is divisible by either 3 or 4?

Solution
20/60+15/60-5/60=30/60=1/2

Mutually Exclusive Events

例一.
Suppose that there are eight runners in a race including John, David and Albert.The probability that John wins the race is 1/2 . David wins the race is 1/4 and Albertwins the race is 1/8. Assume there are no dead heats, find the probability that (a)John or David or Albert wins, (b) neither John nor David wins.

Solution
(a)1/2+1/4 + 1/8=7/8

(b)1-{1/2+1/4}=1/4


例二.
A card is drawn at random from an ordinary pack of 52 playing cards. Find theprobability that the card is (a) a heart or a club, (b) a red card or a club, (c) a redcard or a king.

Solution
(a)13/52+13/52=1/2
(b)26/52+13/52=3/4
(c)26/52+4/52-2/52=7/13