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Nookie1986 [14]
3 years ago
9

. Suppose that 10 students of a class of 50 undergraduates are chosen for a behavioral experiment. The total class consists of 1

5 freshmen, 18 sophomores, 10 juniors, and 7 seniors. If all students are equally likely to be picked, determine the probability of the group contains exactly seven seniors and three juniors.
Mathematics
1 answer:
Natali [406]3 years ago
5 0

Answer:

Approximately 0% probability of the group contains exactly seven seniors and three juniors.

Step-by-step explanation:

A probability is the number of desired outcomes divided by the number of total outcomes.

In this question, the order in which the students are chosen is not important, which means that we use the combinations formula to solve this question.

Combinations formula:

C_{n,x} is the number of different combinations of x objects from a set of n elements, given by the following formula.

C_{n,x} = \frac{n!}{x!(n-x)!}

Desired outcomes:

7 seniors, from a set of 7.

3 juniors, from a set of 10. So

D = C_{7,7} \times C_{10,3} = \frac{7!}{7!(7-7)!} \times \frac{10!}{3!(10-3)&} = 1 \times 120 = 120

Total outcomes:

10 students froms a set of 50. so

T = C_{50,10} = \frac{50!}{10!(50-10)!} = 10272278170

Probability:

p = \frac{D}{T} = \frac{120}{10272278170} \approx 0

Approximately 0% probability of the group contains exactly seven seniors and three juniors.

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Charlie's weight is nine kilograms greater than his brother's. Together they weigh 99 kilograms. Let x represent the weight of t
siniylev [52]


If the weight of the little brother is x, then the weight of  Charles is x + 9

The equation that can be used to determine what each one weighs is:

x + (x + 9) = 99.

Let us now solve it.

x + x +9 = 99

2x + 9 = 99

2x = 99 - 9

2x = 90

x = 90/2

x = 45

Little brother's  weight is 45 kg.

Charles'   weight  will be 45 + 9 =  54 kg

Adding these two weights will give 99kg

 

4 0
3 years ago
Read 2 more answers
A university class has 26 students: 12 are art majors, 9 are history majors, 5 and are nursing majors. The professor is planning
azamat

Answer:

6.9%.

Step-by-step explanation:

Given that a university class has 26 students: 12 are art majors, 9 are history majors, 5 and are nursing majors, and the professor is planning to select two of the students for a demonstration, where the first student will be selected at random, and then the second student will be selected at random from the remaining students, to determine what is the probability that the first student selected is a history major and the second student is a nursing major the following calculations must be performed:

26 = 100

9 = X

9 x 100/26 = X

900/26 = X

34.61 = X

25 = 100

5 = X

500/25 = X

20 = X

0.2 x 0.3461 = X

0.069 = X

Thus, the probability that the first student selected is a history major and the second student is a nursing major is 6.9%.

8 0
3 years ago
Read 2 more answers
A box contains 76 coins, only dimes and nickels. The amount in the box is $4.90. How many dimes and how many nickels are in the
dangina [55]

The number of dimes is 75 coins.

The number of nickels is 1 coin.

<u>Step-by-step explanation:</u>

It is given that,

A box contains 76 coins, only dimes and nickels.

  • The 10 cent coin is called a dime.
  • Let, the number of dimes be x.
  • The 5 cent coin is called a nickel.
  • Let, the number of nickels be y.

<u>This is represented by the system of equations :</u>

x + y = 76  -------(1)

10x + 5y = 4.90  ------(2)

Multiply eq (1) by 5 and subtract eq (2) from eq (1),

 5x + 5y = 380

-<u>(10x + 5y = 4.90)</u>

 <u>-5x       = 375.1</u>

x = 375/5

x = 75 coins.

The number of dimes is 75 coins.

Substitute x=75 in eq (1),

y = 76 - 75

y = 1 coin.

The number of nickels is 1 coin.

6 0
3 years ago
Read 2 more answers
PLEASE HELP I'M TIMED
DedPeter [7]

Really hope i'm right

1st row

the first one is length less than 10

one next to it is width greater than 5

next to that is length greater than 10

2nd row

the first one is length greater than 10

one next to that is width less than 5

next to that is width greater than 5

3rd row

first one is width less than 5

and last is length less than 10

4 0
3 years ago
0000003.09+0000002.1​
Ivanshal [37]

Answer:

5.19

Step-by-step explanation:

6 0
4 years ago
Read 2 more answers
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