In a survey of 300 college graduates, 58% reported that they entered a profession closely related to their college major. If 6 of those survey subjects are randomly selected without replacement for a follow-up survey, what is the probability that 3 of them entered a profession closely related to their college major?

If we select 6 out of 300 subjects, we can assume that the probability remains approximately constant, thus use of the binomial distribution is applicable, where

n=6
p=0.58
bin(6,0.58, 3)
=C(6,3)*0.58^3*0.42^3
=0.2891 approximately

To be more precise, we calculate the probability as:
#ways of choosing 3 out of 174 students who entered a related profession
= C(174,3)
#ways of choosing 3 out of 126 students who entered an unrelated profession
= C(126,3)
#ways of choosing 6 students out of 300
=C(300,6)
So
probability of choosing 3+3 students
= C(174,3)*C(126*3)/C(300,6)
= 0.2917

To find the probability, we need to use the concept of combinations. The formula for combinations is given by:

C(n, r) = n! / (r!(n-r)!)

Where:
n is the total number of items
r is the number of items being chosen

In this case, we have a total of 300 college graduates, and we are selecting 6 of them for the follow-up survey. So n = 300 and r = 6.

The probability of selecting 3 college graduates who entered a profession closely related to their major can be calculated as follows:

P(3 out of 6 entered a related profession) = (C(174, 3) * C(126, 3)) / C(300, 6)

Let's calculate this step-by-step.

Step 1: Calculate the value of C(174, 3)

C(174, 3) = 174! / (3!(174 - 3)!)
= 174! / (3! * 171!)
= (174 * 173 * 172) / (3 * 2 * 1)
= 3,208,824

Step 2: Calculate the value of C(126, 3)

C(126, 3) = 126! / (3!(126 - 3)!)
= 126! / (3! * 123!)
= (126 * 125 * 124) / (3 * 2 * 1)
= 2,090,500

Step 3: Calculate the value of C(300, 6)

C(300, 6) = 300! / (6!(300 - 6)!)
= 300! / (6! * 294!)
= (300 * 299 * 298 * 297 * 296 * 295) / (6 * 5 * 4 * 3 * 2 * 1)
= 19,427,050

Step 4: Calculate the probability

P(3 out of 6 entered a related profession) = (C(174, 3) * C(126, 3)) / C(300, 6)
= (3,208,824 * 2,090,500) / 19,427,050
≈ 0.345882

So, the probability that 3 out of 6 randomly selected college graduates entered a profession closely related to their major is approximately 0.345882.

To find the probability of selecting 3 subjects who entered a profession closely related to their college major, we need to use the concept of combinations.

First, we calculate the total number of ways to choose 6 subjects out of 300. This can be done using the concept of combinations, denoted as "nCk," where n is the total number of objects to choose from and k is the number of objects to choose.

The formula for combinations is given by:

nCr = (n!)/((r!)(n-r)!)

where "!" denotes factorial, indicating the product of all positive integers up to and including the specified number.

In this case, we have n = 300 subjects and k = 6 subjects. Therefore, the total number of ways to choose 6 subjects out of 300 is:

300C6 = (300!)/((6!)(300-6)!)

Next, we need to determine the number of favorable outcomes, which is the number of ways to choose 3 subjects who entered a profession closely related to their college major out of the 58% who reported as such. We can calculate this using the same combination formula, but with n = 174 subjects (58% of 300) and k = 3 subjects:

174C3 = (174!)/((3!)(174-3)!)

Finally, we divide the number of favorable outcomes by the total number of outcomes to obtain the probability:

P(3 out of 6 entered a profession related to their college major) = (174C3)/(300C6)

Now, we can plug in the values and perform the calculations to find the probability.

equation of a line

(-3,5) (-2,-6)

can you help with this exercise