Probability

By TNAll of the calculations base on TI-84 Plus

What’s the probability if randomly selected 1 of the numbers which have 5 digit numbers, greater than 65000, and the number cannot repeat ?

ضطش

FIRST STEP

…

Because we calculate from 65000 to 69000. So that it must has 1 choice.

6 5 0 0 01

At first, we need to know how many number from 65000 to 65999 and the numbers cannot be repeat.

Because we calculate from 65000 to 69000. So that it must has 1 choice.

We have 4 number greater than 5, except 6 (1stnumber).So that it must be 5-1=4

6 5 0 0 01 4

At first, we need to know how many number from 65000 to 65999 and the numbers cannot be repeat.

Because we calculate from 65000 to 69000. So that it must has 1 choice.

We have 4 number greater than 5, except 6 (1stnumber).So that it must be 5-1=4

6 5 0 0 01 4 8

We have 8 numbers to chose (except 2 letters before)

At first, we need to know how many number from 65000 to 65999 and the numbers cannot be repeat.

Because we calculate from 65000 to 69000. So that it must has 1 choice.

We have 4 number greater than 5, except 6 (1stnumber).So that it must be 5-1=4

6 5 0 0 01 4 8

We have 8 numbers to chose (except 2 letters before)

7

We have 7 numbers to chose (except 3 letters before)

At first, we need to know how many number from 65000 to 65999 and the numbers cannot be repeat.

Because we calculate from 65000 to 69000. So that it must has 1 choice.

We have 4 number greater than 5, except 6 (1stnumber).So that it must be 5-1=4

6 5 0 0 01 4 8

We have 8 numbers to chose (except 2 letters before)

7

We have 7 numbers to chose (except 3 letters before)

6

At first, we need to know how many number from 65000 to 65999 and the numbers cannot be repeat.

We have 7 numbers to chose (except 3 letters before)

Because we calculate from 65000 to 69000. So that it must has 1 choice.

We have 4 number greater than 5, except 6 (1stnumber).So that it must be 5-1=4

6 5 0 0 01 4 8

We have 8 numbers to chose (except 2 letters before)

7

We have 7 numbers to chose (except 3 letters before)

6x x x x

Multiply it, we will have the total of number greater than 65000 and smaller than 69999

At first, we need to know how many number from 65000 to 65999 and the numbers cannot be repeat.

We have 7 numbers to chose (except 3 letters before)

Because we calculate from 65000 to 69000. So that it must has 1 choice.

We have 4 number greater than 5, except 6 (1stnumber).So that it must be 5-1=4

6 5 0 0 01 4 8

We have 8 numbers to chose (except 2 letters before)

7

We have 7 numbers to chose (except 3 letters before)

6x x x x

Multiply it, we will have the total of number greater than 65000 and smaller than 69999

At first, we need to know how many number from 65000 to 65999 and the numbers cannot be repeat.

1 x 4 x 8 x 7 x 6 =1344 numbers

We have 7 numbers to chose (except 3 letters before)

SECOND STEP

7,8,9 at 1st position can make the numbers greater than 7000 (the numbers after cannot be repeated => exclude 70000)

0 03

007

Then, we need to know how many number greater than 65999, from 70000 to 99999 and the numbers cannot be repeat.

7,8,9 at 1st position can make the numbers greater than 7000 (the numbers after cannot be repeated => exclude 70000)

0 03

007

Then, we need to know how many number greater than 65999, from 70000 to 99999 and the numbers cannot be repeat.

9

We have 9 numbers to chose (except 1 letters before)

7,8,9 at 1st position can make the numbers greater than 7000 (the numbers after cannot be repeated => exclude 70000)

0 03

007

Then, we need to know how many number greater than 65999, from 70000 to 99999 and the numbers cannot be repeat.

9

We have 9 numbers to chose (except 1 letters before)

8

We have 8 numbers to chose (except 2 letters before)

7,8,9 at 1st position can make the numbers greater than 7000 (the numbers after cannot be repeated => exclude 70000)

0 03

007

Then, we need to know how many number greater than 65999, from 70000 to 99999 and the numbers cannot be repeat.

9

We have 9 numbers to chose (except 1 letters before)

8

We have 8 numbers to chose (except 2 letters before)

7

We have7 numbers to chose (except 3 letters before)

7,8,9 at 1st position can make the numbers greater than 7000 (the numbers after cannot be repeated => exclude 70000)

0 03

007

Then, we need to know how many number greater than 65999, from 70000 to 99999 and the numbers cannot be repeat.

9

We have 9 numbers to chose (except 1 letters before)

8

We have 8 numbers to chose (except 2 letters before)

7

We have7 numbers to chose (except 3 letters before)

6

We have 6 numbers to chose (except 4 letters before)

7,8,9 at 1st position can make the numbers greater than 7000 (the numbers after cannot be repeated => exclude 70000)

0 03

007

Then, we need to know how many number greater than 65999, from 70000 to 99999 and the numbers cannot be repeat.

9

We have 9 numbers to chose (except 1 letters before)

8

We have 8 numbers to chose (except 2 letters before)

7

We have7 numbers to chose (except 3 letters before)

6

We have 6 numbers to chose (except 4 letters before)

x x x x

7,8,9 at 1st position can make the numbers greater than 7000 (the numbers after cannot be repeated => exclude 70000)

0 03

007

Then, we need to know how many number greater than 65999, from 70000 to 99999 and the numbers cannot be repeat.

9

We have 9 numbers to chose (except 1 letters before)

8

We have 8 numbers to chose (except 2 letters before)

7

We have7 numbers to chose (except 3 letters before)

6

We have 6 numbers to chose (except 4 letters before)

x x x x

Multiply it, we will have the total of number greater than 65999 and smaller than 99999 3 x 9 x 8 x 7 x 6=9075

numbers

And now, we add it together to get the 5 digit number greater than 65000.

1344+9072=10416 numbers

To calculate the probability, we need to know how many number have 5 digit number

To calculate the probability, we need to know how many number have 5 digit number

Exclude 0 because if 0 lay at 1st position, it will make the number with 4 digit.

9

To calculate the probability, we need to know how many number have 5 digit number

9

Exclude 0 because if 0 lay at 1st position, it will make the number with 4 digit.

10 10 10 10

The number can be 0 and repeated

To calculate the probability, we need to know how many number have 5 digit number

x x x x9

Exclude 0 because if 0 lay at 1st position, it will make the number with 4 digit.

10 10 10 10

The number can be 0 and repeated

=90000

Multiply it, we will have the total number have 5 digit numbers

PROBABILITY IS 10416/90000

217/1875 (11.57%)