# convert(BADFACED)16 FROM ITS HEXADECIMAL EXPANION TO ITS BINARY EXPANSION

i think you have to convert BAdFACED *16 then the BIanary something.. okay i really don't get this sorry!! **

3 men and 6 women are applying for several jobs. The jobs are book keeper, typist, and translator.

what is the probability that a man will be hired as a translator?

what is the probability that at least 1 man will be hired?

you and your friend are driving down the road. License plates in the state you are in have 3 letters that can repeat followed by 3 digits that can repeat and can also begin with leading zero's .

What is the probability that out of 40 cars, 15 of them will begin with the letter "P"?

PLEASE HELP

10111010110111111010110011101101

## Oh, hex and binary conversion, huh? That's a fun one! Let's break it down.

First, we have the hexadecimal number BADFACED. Now, we need to convert it to binary.

To do that, we can convert each hexadecimal digit to its corresponding binary representation. So, let's take it step by step:

B (11 in decimal) = 1011 in binary

A (10 in decimal) = 1010 in binary

D (13 in decimal) = 1101 in binary

F (15 in decimal) = 1111 in binary

A (10 in decimal) = 1010 in binary

C (12 in decimal) = 1100 in binary

E (14 in decimal) = 1110 in binary

D (13 in decimal) = 1101 in binary

So, when we put them together, we get the binary expansion of BADFACED16 as 10111010110111111010110011101101.

It's like converting a secret code into a different secret code! Binary is just another way to represent numbers using only 0s and 1s. Isn't it fascinating?

Now, let's move on to helping you with those probabilities and license plates!

## To convert the hexadecimal number BADFACED16 to its binary expansion, you can follow these steps:

1. Identify the hexadecimal digits: B, A, D, F, A, C, and E.

2. Convert each hexadecimal digit to its equivalent 4-bit binary representation:

B = 1011

A = 1010

D = 1101

F = 1111

A = 1010

C = 1100

E = 1110

3. Concatenate the binary representations of each hexadecimal digit:

Binary expansion of BADFACED16 = 10111010110111111010110011101101

Therefore, the binary expansion of BADFACED16 is 10111010110111111010110011101101.

Now, let's move on to your other questions:

1. Probability that a man will be hired as a translator:

Since there are 3 men and 6 women applying for jobs, the total number of applicants is 3 + 6 = 9.

Assuming all applicants have an equal chance of being hired, the probability that a man will be hired as a translator is 3/9 = 1/3.

2. Probability that at least 1 man will be hired:

To calculate the probability that at least 1 man will be hired, we need to consider two scenarios:

- Scenario 1: Only 1 man is hired, and the remaining positions are filled by women.

The probability of this scenario can be calculated as (3/9) * (6/8) * (5/7) = 15/168.

- Scenario 2: More than 1 man is hired, and the remaining positions are filled by women.

The probability of this scenario can be calculated as 1 - (probability of no man being hired).

The probability of no man being hired is (6/9) * (5/8) * (4/7) = 60/168.

So, the probability of more than 1 man being hired is 1 - 60/168 = 108/168.

The total probability of at least 1 man being hired is the sum of the probabilities from Scenario 1 and Scenario 2:

Total probability = (15/168) + (108/168) = 123/168.

3. Probability that out of 40 cars, 15 of them will begin with the letter "P":

Assuming each letter and digit has an equal chance of being selected for a license plate, the probability of each letter being "P" is 1/26. Since there are 3 letters in a license plate, the probability that a license plate begins with "P" is (1/26)^3.

Therefore, the probability that out of 40 cars, 15 of them will begin with the letter "P" can be calculated using the binomial probability formula:

P(X = 15) = (40 choose 15) * ((1/26)^3)^15 * (1 - (1/26)^3)^(40-15),

where (40 choose 15) represents the combination of choosing 15 license plates out of 40.

To calculate this probability, you can use a calculator or a statistical software package.

## To convert the hexadecimal number BADFACED16 to its binary expansion, you can follow these steps:

1. Write down the hexadecimal number: BADFACED.

2. Convert each hexadecimal digit to its binary equivalent:

B = 1011

A = 1010

D = 1101

F = 1111

A = 1010

C = 1100

E = 1110

D = 1101

3. Concatenate the binary equivalents of each hexadecimal digit to get the binary expansion:

10111010110111111010110011101101

So, the binary expansion of BADFACED16 is 10111010110111111010110011101101.

Now let's move on to the probabilistic questions.

Question 1: What is the probability that a man will be hired as a translator?

To find the probability, we need to know the total number of applicants and the number of men applying for the job of translator.

If there are 3 men and 6 women applying for the jobs, and we assume an equal probability for each individual to be hired, then there are 9 people in total. Since we don't know how many of them are applying for the position of translator, we cannot determine the exact probability without that information.

Question 2: What is the probability that at least 1 man will be hired?

To find the probability, we need to know the total number of applicants, the number of men, and the conditions for hiring.

If the number of men and women remains the same (3 men and 6 women) and we assume an equal probability for each individual to be hired, then the total number of possible outcomes is the total number of ways the 9 people can be hired, which is 9!.

To find the probability that at least one man will be hired, we need to calculate the number of cases where at least one man is hired and divide it by the total number of possible outcomes.

To calculate the number of cases where at least one man is hired, we can subtract the number of cases where all women are hired from the total number of possible outcomes.

Number of cases where all women are hired: 6!

Therefore, the probability that at least one man will be hired is (9! - 6!) / 9!.

I'm sorry, but I cannot answer the third question about the probability of license plates beginning with the letter "P" without knowing the total number of possible license plates in the state. Please provide that information, and I will be happy to help you calculate the probability.