Maths

2. The required probability
=P($2, $2)+P($1, $2)+P($2, $1)
=2/7*1/6+3/7*2/6+2/7*3/6
=14/42
=1/3

3(a) Condition=(1,1), (2,2), (3,3), (4,4), (5,5), (6,6)
The required probability
=2/6
=1/3

(b) Condition=(3,6), (4,5), (4,6), (5,4), (5,5), (5,6), (6,3), (6,4), (6,5), (6,6)
The required probability
=2/10
=1/5

2.There is 8 coins in the purse totally. It means that there are 7C2=7!/[2!(7-2)!]=21 combinations.
If one or more fifty-cent coin(s) is/are taken, the following types of combinations will be formed:
$(0.5+0.5)=$1<$2.5
$(0.5+1)=$1.5<$2.5
$(0.5+2)=$2.5
Neither one of them are greater than $2.5.
The following types of combinations are greater than $2.5.
$(1+2)=$3>2.5
$(2+2)=$4>2.5
There are 3 one-dollar coins and 2 two-dollar coins in the purse so there are 3*2=6 combinations. There are only 2 two-dollar coins so there's only one combination. There are 7 combinations totally.
Probability that the total value of the two coins is greater than $ 2.5
=7/28
=1/4
=25%
3a. Only 6 results of the number shown on the two dice will be the same. And only 5,5 and 6,6 are greater than 8.
So the probability that the sum of the two numbers is greater than 8
=2/6
=1/3
3b.It means the sum of the two numbers that show up is between 9-12. Only the following results are greater than 8:
(3,6),(4.5),(4,6),(5,5),(5,6),(6,6)
Only the fourth and sixth result satisfy the question.
So the probability that the two numbers are the same
=2/6
=1/3

2007-10-21 22:25:58 補充：
3b.It means the sum of the two numbers that show up is between 9-12. Only the following results are greater than 8: (3,6),(4.5),(4,6),(5,4),(5,5),(5,6),(6,3),(6,4),(6,5),(6,6)The permutation is also inportant.2/10=20%