Mathematics, 21.08.2019 00:30 kaileyy06

6) an urn contains eight green balls and nine white balls. a sample of four balls is selected at random from the urn.
(a) find the probability that the four balls have the same color.
(b) find the probability that the sample contains more green balls than white balls.
(a) the probability that the four balls have the same color is

Answers: 3

Show answers

Answers

Answer from: lilyclairehutson

Using the hypergeometric distribution, it is found that there is a:

a) 0.0893 = 8.93% probability that the four balls have the same color.

b) 0.2412 = 24.12% probability that the sample contains more green balls than white balls.

The balls are chosen without replacement, which means that the hypergeometric distribution is used to solve this question.

Hypergeometric distribution:

$P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}$

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

The parameters are:

x is the number of successes. N is the size of the population. n is the size of the sample. k is the total number of desired outcomes.

In this problem:

The urn contains 8 + 9 = 17 balls, thus N = 17

.Eight of those are green, thus k = 8

4 are going to be selected, thus n = 4

Item a:

Same color is none green, all white, which is P(X = 0), or all green, which is P(X = 4). Then:

p = P(X = 0) + P(X = 4)

In which:

$P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}$

$P(X = 0) = h(0,17,4,8) = \frac{C_{8,4}C_{9,0}}{C_{17,4}} = 0.0529$

$P(X = 4) = h(4,17,4,8) = \frac{C_{8,0}C_{9,4}}{C_{17,4}} = 0.0294$

p = P(X = 0) + P(X = 4) = 0.0529 + 0.0294 = 0.0893

0.0893 = 8.93% probability that the four balls have the same color.

Item b:

This is the probability of at least 3 green balls, thus:

$P(X \geq 3) = P(X = 3) + P(X = 4)$

In which:

$P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}$

$P(X = 3) = h(3,17,4,8) = \frac{C_{8,1}C_{9,3}}{C_{17,4}} = 0.2118$

$P(X = 4) = h(4,17,4,8) = \frac{C_{8,0}C_{9,4}}{C_{17,4}} = 0.0294$

Then:

$P(X \geq 3) = P(X = 3) + P(X = 4) = 0.2118 + 0.0294 = 0.2412$

0.2412 = 24.12% probability that the sample contains more green balls than white balls.

A similar problem is given at link

Answer from: rick4763

There is a total of 17 balls in the urn, and there are $\dbinom{17}4=\dfrac{17!}{4!(17-4)!}=2380$ ways of selecting 4 balls from it.

$P(\text{all green OR all white})=P(\text{all green})+P(\text{all white})=\dfrac{\binom84+\binom94}{\binom{17}4}=\boxed{\dfrac7{85}}$

$P(\text{3 green, 1 white OR all green})=P(\text{3 green, 1 white})+P(\text{all green})=\dfrac{\binom83\binom91+\binom84}{\binom{17}4}=\boxed{\dfrac{41}{170}}$

Answer from: Quest

i think c. but don't trust it.

step-by-step explanation:

Answer from: Quest

answer:

payment just for service

→

87.12

payment for service including tax

→

94.09

explanation:

service only with 20% tip

→

72.6

(

100

)

87.12

in the opening of the question the word 'service' is associated only with the pretax value.

the closing part of the question asks: how much did she pay for the

service

−−−−−−

so technically the answer is

→

72.6

(

100

)

87.12

however, the intention of the question provider may have been that your answer is to be

87.12

(

100

)

94.09

to 2 decimal places.

payment just for service

→

87.12

payment for service including tax

→

94.09

tony b

mar 21, 2017

answer:

trying to explain it another way

explanation:

service charge

→

72.60

20% tip

100

72.60

14.52

−−−−−−

←

add

87.12

tax

100

87.12

6.97

−−−−−

←

add

94.09

Another question on Mathematics

Mathematics, 21.06.2019 14:30

Click on the graphic until you find the right quotient. (36xa - 30xb) ÷ (-6x2)

Answers: 3

Answer

Mathematics, 21.06.2019 20:00

Landon wrote that 3−2.6=4. which statement about his answer is true?

Answers: 1

Answer

Mathematics, 21.06.2019 23:30

Matt had 5 library books. he checked out 1 additional book every week without retuening any books. whats the matching equation

Answers: 1

Answer

Mathematics, 22.06.2019 03:30

Use the method of cylindrical shells to find the volume v generated by rotating the region bounded by the given curves about y = 8.8y = x3, y = 0, x = 4use the method of cylindrical shells to find the volume v generated by rotating the region bounded by the given curves about y = 8.8y = x3, y = 0, x = 4

Answers: 1

Answer

You know the right answer?

6) an urn contains eight green balls and nine white balls. a sample of four balls is selected at ran...

Questions