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snow_tiger [21]
2 years ago
12

A box has five items, three good and two defective. three items are selected at random without replacement. let x be the number

of defective items selected. find the probability mass function of x.
Mathematics
1 answer:
user100 [1]2 years ago
7 0
This problem can be solved from first principles, case by case.  However, it can be solved systematically using the hypergeometric distribution, based on the characteristics of the problem:
- known number of defective and non-defective items.
- no replacement
- known number of items selected.

Let
a=number of defective items selected
A=total number of defective items
b=number of non-defective items selected
B=total number of non-defective items
Then 
P(a,b)=C(A,a)C(B,b)/C(A+B,a+b)
where 
C(n,r)=combination of r items selected from n,
A+B=total number of items
a+b=number of items selected

Given:
A=2
B=3
a+b=3
PMF:
P(0,3)=C(2,0)C(3,3)/C(5,3)=1*1/10=1/10
P(1,2)=C(2,1)C(3,2)/C(5,3)=2*3/10=6/10
P(2,0)=C(2,2)C(3,1)/C(5,3)=1*3/10=3/10
Check: (1+6+3)/10=1 ok
note: there are only two defectives, so the possible values of x are {0,1,2}

Therefore the 
PMF:
{(0, 0.1),(1, 0.6),(2, 0.3)}

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Using proportions, considering the weight of each bar and the ratio, it is found that the ship is carrying 52 gold bars.

<h3>What is a proportion?</h3>

A proportion is a fraction of a total amount, and the measures are related using a rule of three.

Each bar weighs 5 kg, and the total weight is of 600 kg, hence the number of bars is given by:

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The proportion of gold bars is given by:

p = 13/(13 + 17) = 13/30

Hence, out of 120 bars, the number of gold bars is given by:

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More can be learned about proportions at brainly.com/question/24372153

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A number increased by 3 and then multiplied by 5 is at least -10. What are the three lowest natural number values this can be?
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Step-by-step explanation:

It is impossible for the number values of this number to be a natural number since natural numbers are defined as being positive integers while the number "x" has to be less than -5 to satisfy the equation.

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3 years ago
If the first number is increased by 7 and the second number is reduced by 6 times, the sum of these numbers is 29.
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Answer:

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Explanation:

Let the 1st number be x

Let the 2nd number be y

=====================

Condition 1

\sf \rightarrow  x + 7 + \dfrac{y}{6}  = 29

\rightarrow \sf x=-\dfrac{y}{6}+22

=====================

Condition 2

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=====================

Substitute equations

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=====================

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Step-by-step explanation:

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