Introduction to Probability

Question

Please to solve the following questions:

1. A positive integer lessthan 21 is chosen at random. What is the probability

that it is a multiple of 3?

2. Which of the following numbers can represent the probability of an event?

a. 3.1415/2 b. 1/3.1415 c. 1/2^1

3.A card is drawn at random from a pack of well-shuffled playing cards. What

is the probability of getting a Jack or a spade?

4.If two dice are rolled, the probability of getting a sum divisible by 4 is

5.A series of literature books contains 4 volumes, and they are arranged on a bookshelf at random. Whant is the probability that the first and the last volume are placed at both ends?

Answer 1

最愛解答

1.

P(multiple of 3)

=P(getting 3,6,9,12,15,18)

=6/20

=3/10

2.

1/3.1415 and 1/2^1 can represent a probability of event.

(The values of above numbers are between 0 and 1)

3.

P(Jack or spade)

=P(spade)+P(Jack)-P(spade Jack)

=13/52+4/52-1/52

=16/52

=4/13

4.

P(divisible by 4)

=P(get 4)+P(get 8)+P(get 12)

=P(get (1,3)or(2,2)or(3,1))+P(get (2,6)or(3,5)or(4,4)or(5,3)or(6,2))+P(get(6,6))

=3/36+5/36+1/36

=9/36

=1/4

5.

P(first, last volume are at both ends)

=P(first volume at end A, then last volume at end B)+P(first volume at end B then last volume at end A)

=(1/4)(1/3)+(1/4)(1/3)

=1/12+1/12

=1/6