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Butoxors [25]
3 years ago
7

a jar contains ten black buttons and six brown buttons. If nine buttons are picked at random, what is the probability that exact

ly five of them are black?
Mathematics
1 answer:
Anuta_ua [19.1K]3 years ago
6 0

Answer:

33.04% probability that exactly five of them are black

Step-by-step explanation:

A probability is the number of desired outcomes divided by the number of total outcomes.

The order in which the buttons are chosen is not important. So we use the combinations formula to solve this question.

Combinations formula:

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

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

Desired outcomes:

Five black buttons, from a set of 10

Four brown buttons, from a set of 6.

D = C_{10,5}*C_{6,4} = \frac{10!}{5!(10-5)!}*\frac{6!}{4!(6-4)!} = 3780

Total outcomes:

Nine buttons, from a set of 16.

T = C_{16,9} = \frac{16!}{9!(16-9)!} = 11440

Probability:

p = \frac{D}{T} = \frac{3780}{11440} = 0.3304

33.04% probability that exactly five of them are black

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Step-by-step explanation:

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3 years ago
A probability experiment is conducted in which the sample space of the experiment is upper s equals startset 4 comma 5 comma 6 c
olchik [2.2K]
The correct question statement is:

A probability experiment is conducted in which the sample space of the experiment is S = {4,5,6,7,8,9,10,11,12,13,14,15}. Let event E={7,8,9,10,11,12,13,14,15}. Assume each outcome is equally likely. List the outcomes in E^{c}. Find P(E^{c}).

Solution:

Part 1:

E^{c} means compliment of the set E. A compliment of a set can be obtained by finding the difference of the set from the universal set. The universal set is the set which contains all the possible outcomes of the events which is S in this case.

So, compliment of E will be equal to S - E. S - E will result in all those elements of S which are not present in E. So, we can write:

E^{c}=S-E \\  \\ 
E^{c}=(4,5,6,7,8,9,10,11,12,13,14,15)-(7,8,9,10,11,12,13,14,15) \\  \\ 
E^{c}=(4,5,6)

Thus the set compliment of E will contain the elements {4,5,6}.So

E^{c} = {4,5,6}

Part 2)

P(E^{c}) means probability that if we select any number from the Sample Space S, it will belong the set E compliment.

P(E^{c}) = (Number of Elements in E^{c})/Number of elements in S

Number of elements in set S = n(S) = 12
Number of elements in set E^{c} = n(E^{c})=3

So, 

P(E^{c})= \frac{n(E^{c}) }{n(S)} \\  \\ 
P(E^{c})= \frac{3}{12} \\  \\ 
P(E^{c})= \frac{1}{4}
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3 years ago
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Step-by-step explanation:

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2 years ago
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Answer:

Step-by-step explanation:

If given tables in the picture show the proportional relationship,

Number of wheels (w) ∝ Number of buses (b)

w ∝ b

w = kb

Here, k = proportionality constant

k = \frac{w}{b}

Number of buses (b)           Number wheels (w)             Wheels per bus (\frac{w}{b})

          5                                           30                               \frac{30}{5}=6              

          8                                           48                               \frac{48}{8}=6

         10                                           60                               \frac{60}{10}=6

         15                                           90                               \frac{90}{15}=6

Here, proportionality constant is 6.

Similarly, If number of wheels (w) ∝ Number of train cars (t)

w = kt

Here, k = proportionality constant

k = \frac{w}{t}

Number of train cars(t)          Number of wheels(w)     Wheels per train car (\frac{w}{t})

              20                                        184                           \frac{184}{20}=9.2

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              50                                        424                           \frac{424}{50}=8.48

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3 years ago
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Answer:

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Step-by-step explanation:

The simplest way to determine is testing out the numbers with Pythagorian theorem.

If it complies with the theorem, it is a right triangle.

let's assume c = 28, b = 21, and a = 20

the longest side is the hypotenuse so side c (28 in) will be the hypotenuse.

According to the Pythagorian theorem, the square of the length of hypotenuse must equal to the sum of squares of other two sides.

check:

c^2 = 28^2 = 784

a^2 + b^2 = 21^2 + 20^2 = 841

because c^2 is not equal to a^2 + b^2, the triangle is not a right triangle.

7 0
3 years ago
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