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____ [38]
3 years ago
10

We roll a fair die repeatedly until we see the number four appear and then we stop. The outcome of the experiment is the number

of rolls.a. Describe a sample space Ohm and a probability measure P to model this situation. b. Calculate the probability that the number four never appears.
Mathematics
1 answer:
muminat3 years ago
8 0

Answer:

0

Step-by-step explanation:

given that we roll a fair die repeatedly until we see the number four appear and then we stop.

the number 4 can appear either in I throw, or II throw or .... indefinitely

So X = the no of throws can be from 1 to infinity

This is a discrete distribution countable.

Sample space= {1,2,.....}

b) Prob ( 4 never appears) = Prob (any other number appears in all throws)

= \frac{5}{6} *\frac{5}{6} *\frac{5}{6} *\frac{5}{6} *...\\=(\frac{5}{6} )^n

where n is the number of throws

As n tends to infinity, this becomes 0 because 5/6 is less than 1.

Hence this probability is approximately 0

Or definitely 4 will appear atleast once.

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Un empresario textil de Gamarra desea distribuir un bono de productividad entre sus empleados por su buen desempeño en la semana
spin [16.1K]

Answer:

There are 6 employees in the factory

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Question:

A textile entrepreneur from Gamarra wants to distribute a productivity bonus among his employees for his good

performance in the week. Making calculations, he realizes that if he gave each one 800 soles, he would have

200 leftovers , and if he gave them 900 soles, he would lack 400. How many employees are there in your factory? How much money do you have to distribute? How would you solve the problem without using equations?

Step-by-step explanation:

For the first two questions, we would determine the number of employees that are in the factory and the amount of money that was distributed by solving using equations. Each statement would be written in the form of an equation.

Let the amount of money distributed to the employees = p

The number of employees in the factory = q

First statement showing the relationship of the variables:

800q + 200 = p ...equation 1

2nd statement showing the relationship of the variables:

900q - 400 = p ...equation 2

Equating both equations: p = p

800q + 200 = 900q - 400

900q-800q = 200+400

100q = 600

q = 600/100 = 6

Substitute for q = 6 in any if the equation.

Using equation 1

800(6) + 200 = p

p = 5000

Therefore, the amount of money distributed to the employees = 5000soles

The number of employees in the factory = 6

To solve the problem without using equations, We would try different numbers for the employees starting from 2 employees (as they are more than 1) to arrive at a particular amount distributed:

(800×2) + 200 = 1800

(900×2) - 400 = 1400

By increasing the numbers using consecutive even numbers (2,4,6...) and multiplying, we would arrive at a value that is equal to both.

8 0
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