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marshall27 [118]
3 years ago
10

Suppose each laptop of a certain type is assigned a series number, which consists of a sequenceof eight symbols: number, letter,

letter, letter, number, number, number, number, where aletter is any one of 26 letters and a number is one among 0, 1,. . ., 9. Assume that all series numbers are equally likely.
(a) What is the probability that all symbols are different if one laptop is picked at random with equal probability?
(b) What is the probability that all symbols are different and the first number is the largest among the numbers?
Mathematics
1 answer:
Varvara68 [4.7K]3 years ago
5 0

Answer:

Step-by-step explanation:

There are 5numbers and 3 letters. Each number can be one among the 10 possible.

Each letter is 1 among the 26 available.

a)The number of possible unique serial numbers are

10^5x 26³

The number of 5 number combinations each different (order important) is 5!(10/5)= 30240

The number of 3 letter combinations each different (order important) is 3!(26/3)=15600

The required probability (that all symbols are different if one laptop is picked at random with equal probability) is

15600x3240/ 10^5x 26³=0.2684

b) The first letter must be at least 4 to be largest among the 5 numbers. So the first letter can be one of . 4,5,6,7,8,9..

The number of 5 number combinations each different and starting with 4 (order important) is .

4!=24

The number of 5 number combinations each different and starting with 5 (order important) is .

4!(5/4)= 120

The number of 5 number combinations each different and starting with 6 (order important) is .

4!(6/4)= 360

The number of 5 number combinations each different and starting with 7 (order important) is .

4!(7/4)= 840

The number of 5 number combinations each different and starting with 8 (order important) is

4!(8/4)= 1680

The number of 5 number combinations each different and starting with 9 (order important) is .

4!(9/4)= 3024

Thus, there are

The required probability ( that all symbols are different and the first number is the largest among the numbers) is

15600* 6040/10^5x 26³= 0.0537

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Music Company A charges a $15 membership fee and $0.75 each to download a song. Music Company B charges $0.90 each to download a
Contact [7]

The number of songs that both companies will charge the same amount is 100. And to pay the least amount of money we need to choose Company B.

<h3>Linear Equation: </h3>

The mathematical expressions that we used to find unknown numbers are called Linear Equations. These can be formed by variables and constant terms according to given conditions. Here we use variables like x, y, z, etc to represent unknown variables.

 

Here we have,

Music company A charges a $ 15 membership fee and a $ 0.75 for each downloaded song

Music company B charges $ 0.90 for each downloaded song without the membership fee

Given question

a. For what number of songs will both companies charge the same amount?  

Let for x songs both companies will charge the same amount

Cost to download x songs from Company A

=> 15 + 0.75x

Cost to download x songs from Company B

=>  0.90x

As we assumed both costs are the same

=> 15 + 0.75x = 0.90x

=> 0.90x - 0.75 = 15

=> 0.15x = 15

-> x = 100

Therefore,

The number of songs that both companies will charge the same amount is 100.

b) You anticipate that you will download 150 songs. Which company should you choose if you want to spend the least amount of money?  

Cost of 150 that charges company A =  15 + 150(0.75)  

= 15 + 150(0.75)  = 15 + 112.5 = 127.5  

Therefore,

Company A will charge $ 127.5 for 150 songs

Cost of 150 songs that charges company B = 150(0.90)

= $ 135  

Company B will charge $ 135 for 150 songs

Therefore,

Company B will charge $ 135 for 150 songs

Thus,

To pay the least amount of money we need to choose Company B.

Therefore,

The number of songs that both companies will charge the same amount is 100. And to pay the least amount of money we need to choose Company B.

Learn more about Linear Equations at

brainly.com/question/11897796

#SPJ4

3 0
1 year ago
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