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rosijanka [135]
3 years ago
13

A standard six-sided die is rolled $6$ times. You are told that among the rolls, there was one $1,$ two $2$'s, and three $3$'s.

How many possible sequences of rolls could there have been? (For example, $3,2,3,1,3,2$ is one possible sequence.)
Mathematics
1 answer:
Alex777 [14]3 years ago
7 0

Answer:

Sequence = 120

Step-by-step explanation:

Given

6 rolls of a die;

Required

Determine the possible sequence of rolls

From the question, we understand that there were three possible outcomes when the die was rolled;

The outcomes are either of the following faces: 1, 2 and 3

Total Number of rolls = 6

Possible number of outcomes = 3

The possible sequence of rolls is then calculated by dividing the factorial of the above parameters as follows;

Sequence = \frac{6!}{3!}

Sequence = \frac{6 * 5 * 4* 3!}{3!}

Sequence = 6 * 5 * 4

Sequence = 120

Hence, there are 120 possible sequence.

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A food-packaging apparatus underfills 10% of the containers. Find the probability that for any particular 10 containers the numb
Maksim231197 [3]

Answer:

a) P(X = 1) = 0.38742

b) P(X = 3) = 0.05740

c) P(X = 9) = 0.00000

d) P(X \geq 5) = 0.00163

Step-by-step explanation:

For each container, there are only two possible outcomes. Either it is undefilled, or it is not. This means that we can solve this problem using the binomial probability distribution.

Binomial probability distribution:

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

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

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

And p is the probability of X happening.

In this problem

There are 10 containers, so n = 10.

A food-packaging apparatus underfills 10% of the containers, so p = 0.1.

a) This is P(X = 1)

P(X = 1) = C_{10,1}.(0.1)^{1}.(0.9)^{9} = 0.38742

b) This is P(X = 3)

P(X = 3) = C_{10,3}.(0.1)^{3}.(0.9)^{7} = 0.05740

c) This is P(X = 9)

P(X = 9) = C_{10,9}.(0.1)^{9}.(0.9)^{1} = 0.00000

d) This is P(X \geq 5).

Either the number is lesser than five, or it is five or larger. The sum of the probabilities of each event is decimal 1. So:

P(X < 5) + P(X \geq 5) = 1

P(X \geq 5) = 1 - P(X < 5)

In which

P(X < 5) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4)

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

P(X = 0) = C_{10,0}.(0.1)^{0}.(0.9)^{10} = 0.34868

P(X = 1) = C_{10,1}.(0.1)^{1}.(0.9)^{9} = 0.38742

P(X = 2) = C_{10,2}.(0.1)^{2}.(0.9)^{8} = 0.1937

P(X = 3) = C_{10,3}.(0.1)^{3}.(0.9)^{7} = 0.05740

P(X = 4) = C_{10,4}.(0.1)^{1}.(0.9)^{9} = 0.38742

So

P(X < 5) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) = 0.34868 + 0.38742 + 0.19371 + 0.05740 + 0.01116 = 0.99837

Finally

P(X \geq 5) = 1 - P(X < 5) = 1 - 0.99837 = 0.00163

3 0
3 years ago
What is the value of 5a + 7b <br> if a = 4 and b = 3?? <br> a : 41<br> b : 12<br> c : 43 <br> d : 35
MAXImum [283]
<h3>Answer:</h3><h3>41</h3><h3>Step-by-step explanation:</h3><h3>multiplication and addition</h3><h3>5x4=20</h3><h3>7x3=21</h3><h3>20+21=41</h3>
8 0
2 years ago
Read 2 more answers
A local movie theater is selling movie tickets for $5.25 during the first week of May. The regular price of a ticket is $6.75. W
Phantasy [73]

Answer:

7

Step-by-step explanation:

8

6 0
3 years ago
You have a right circular cone of height 1530 mm and volume 2.2 x 104 in3 . Calculate the base diameter of the cone.
Alja [10]

Answer:

  37.35 in

Step-by-step explanation:

The volume of a cone is given by the formula ...

  V = (π/3)r²h

where r is the radius of the base and h is the height. We want to find the diameter of the base, so we can rewrite this in terms of diameter and solve for d. Please note that the height is given in millimeters, not inches, so a conversion is necessary.

  V = (π/3)(d/2)²h

  12V/(πh) = d²

  d = 2√(3V/(πh)) = 2√(3(2.2×10^4 in^3)/(π·1530 mm/(25.4 mm/in))

  = 2√(1.6764×10^6/(π·1.53×10^3) in^2)

  d ≈ 37.35 in

The base diameter of the cone is about 37.35 inches.

4 0
3 years ago
Select all of the transformations that could change the location of the asymptotes of a cosecant of secant
77julia77 [94]

Answer:

phase shift and period change

Step-by-step explanation:

just did it

4 0
3 years ago
Read 2 more answers
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