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3 years ago

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Mathematics

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algol133 years ago

7 0

Answer:

Step-by-step explanation:

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A collection of 30 gems, all of which are identical in appearance, are supposedto be genuine diamonds, but actually contain 8 wo

levacccp [35]

Answer:

Step-by-step explanation:

From the given information:

There are 30 collections of gems, of which 8 are worthless;

Thus, the number of the genuine diamonds = 30 - 8 = 22.

Let X = random variable;

X consider the value as 0 (for 2 worthless stone selection),

X = 1200(1 worthless stone & 1 genuine stone)

X = 2400 (2 genuine stones selected)

However, the numbers of ways of selecting and chosen Gems can be estimated as:

$(^n_r) = (^{30}_2) \\ \\ \implies \dfrac{30!}{2!(30-2)!} \\ \\ \implies \dfrac{30!}{2!(28)!} \\ \\ \implies \dfrac{30*29*28!}{2!(28)!} \\ \\ \implies \dfrac{30*29}{2*1} \\ \\ \implies 435$

Thus;

$Pr (X = 0) = \dfrac{(^8_2)}{435}$

$Pr (X = 0) = \dfrac{\dfrac{8!}{2!(8-2)!}}{435} \\ \\ Pr (X = 0) = \dfrac{\dfrac{8!}{2!(6)!}}{435} \\ \\ Pr (X = 0) = \dfrac{\dfrac{8*7*6!}{2!(6)!}}{435} \\ \\ Pr (X = 0) = \dfrac{\dfrac{8*7}{2*1}}{435} \\ \\ Pr (X = 0) = 0.0644$

$P(X =1200) = \dfrac{(^{8}_{1})(^{22}_{1})}{435}$

$P(X =1200) = \dfrac{ \dfrac{8!}{1!(8-1)!}) ( \dfrac{22!}{1!(22-1)!}) }{435}$

$P(X =1200) = \dfrac{ (8) ( 22) }{435}$

$P(X =1200) =0.4046$

$Pr (X = 2400) = \dfrac{(^{22}_2)}{435}$

$Pr (X = 2400) = \dfrac{\dfrac{22!}{2!(22-2)!}}{435} \\ \\ Pr (X = 2400) = \dfrac{\dfrac{22!}{2!(20)!}}{435} \\ \\ Pr (X = 2400) = \dfrac{\dfrac{22*21*20!}{2!(20)!}}{435} \\ \\ Pr (X =2400) = \dfrac{\dfrac{22*21}{2*1}}{435} \\ \\ Pr (X = 2400) = 0.5310$

To find E(X):

E(X) = (0 × 0.0644) + (1200 × 0.4046) + (2400 × 0.5310)

E(X) = 0 + 485.52 + 1274.4

E(X) = 1759.92

8 0

3 years ago

A recent poll found that 35% of those surveyed are worried about aggressive drivers on the road. If three people are selected at

Ugo [173]

The probability that all three people surveyed is an independent probability and the calculated probability is 0.1225

The probability a surveyed driver is worried = 35%

P(worried) = 0.35

Number of people surveyed = 3

Since the probability of being worried is independent ;

Probability = P(A) × P(B) × P(C)

The probability that all 3 surveyed are worried :

P(worried) × P(worried) × P(worried)
(0.35 × 0.35 × 0.35) = 0.1225

Therefore, the probability that all three people surveyed are worried is : 0.1225

Learn more : brainly.com/question/18153040

5 0

2 years ago

Need the Answer quickly

tensa zangetsu [6.8K]

the answer is B because it's B

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2 years ago

Helppp! Again! Please!!

erastovalidia [21]

Answer:

pretty sure its 6, i think

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3 years ago

In ΔHIJ, i = 550 inches, j = 150 inches and ∠H=92°. Find the length of h, to the nearest inch.

Novay_Z [31]

Answer:575

Step-by-step explanation: deltamath

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2 years ago