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matrenka [14]
3 years ago
10

At a blind taste competition a contestant is offered 3 cups of each of the 3 samples of tea in a random arrangement of 9 marked

cups. If each contestant tastes 4 different cups of tea, what is the probability that a contestant does not taste all of the samples?A. 1/12B. 5/14C. 4/9D. 1/2E. 2/3
Mathematics
1 answer:
solmaris [256]3 years ago
4 0

Answer:

\frac{5}{14}

Step-by-step explanation:

Data provided in the question:

Number of cups of tea offered = 3

Number of cups marked = 9

Number of cups tasted by each = 4

Now,

The probability that a contestant does not taste all of the samples

= contestant tastes only 2 samples of tea

= \frac{C_3^2\timesC_6^4}{C_9^4}

C₆⁴ = number of ways to choose 4 cups out of 6 cups of two samples

C₃² = number of ways to choose which 2 samples will be tasted

[ as 2 samples × 3 cups each = 6 cups ]

C₉⁴ = Number of ways to choose 4 cups out of 9

= \frac{5}{14}

Hence,

the correct answer is option (B) 5/14

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2.- Supóngase que los diámetros de los tornillos fabricados por una compañía están distribuidos normalmente con una media de 0.2
Sergio [31]

Answer:

7.30167%

Step-by-step explanation:

Usando la fórmula de puntuación z

z = (x-μ) / σ, donde x es la puntuación bruta, μ es la media de la población y σ es la desviación estándar de la población

Para x <0.20 pulgadas

z = 0.20 - 0.25 / 0.02

z = -2.5

Valor de probabilidad de Z-Table:

P (x <0.20) = 0.0062097

Para x> 0.28 pulgadas

z = 0.28 - 0.20 / 0.02

z = 1.5

Valor de probabilidad de Z-Table:

P (x <0.28) = 0.93319

P (x> 0.28) = 1 - P (x <0.28) = 0.066807

La probabilidad de que se produzcan tornillos defectuosos cuando el tornillo se considera defectuoso si su diámetro es inferior a 0.20 pulgadas o superior a 0.28 pulgadas es

P (x <0.20) + P (x> 0.28)

= 0.0062097 + 0.066807

= 0.0730167

Conversión a porcentaje

= 0.0730167 × 100

= 7.30167%

El porcentaje de tornillos defectuosos producidos es

7.30167%

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Answer:

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Step-by-step explanation:

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Step-by-step explanation:

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