Probability question.

- mathmath333

Probability question.

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- mathmath333

\(\large \color{black}{\begin{align}& \normalsize \text{A box contains 10 red marbles, 20 blue marbles and 30 green marbles}\hspace{.33em}\\~\\
& \normalsize \text{5 marbles are drawn from the box}\hspace{.33em}\\~\\
& \normalsize \text{what is the probability that } \hspace{.33em}\\~\\
& \normalsize \text{(i) atleast one will be green?}\hspace{.33em}\\~\\
\end{align}}\)

- ganeshie8

may be work the probability for "none will be green"
then subtract that from 1

- mathmath333

phi is a person , he is not a method

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## More answers

- mathmath333

but substracting from (1- "none will be green")
Will resemble all will be green

- ganeshie8

whats the negation of "none of them are green" ?

- ganeshie8

do you say "none of them are green" to below set ?
{B R B R G B}
?

- mathmath333

All will be green ?
Or
At least one will be green .
i am confused

- mathmath333

\(\color{blue}{\text{Originally Posted by}}\) @ganeshie8
do you say "none of them are green" to below set ?
{B R B R G B}
?
\(\color{blue}{\text{End of Quote}}\)
one G is green.

- ganeshie8

negation of "none of them are green"
is
"at least one of them is green"

- mathmath333

ok my english / logic is weak.

- ganeshie8

your english/logic is fine, it takes some to see why above is true
lets do some examples may be

- mathmath333

ok

- ganeshie8

whats the opposite of statement : "all of them are green"

- ganeshie8

whats the opposite of statement : "all of them did good"

- mathmath333

none of them is green

- ganeshie8

wrong

- mathmath333

y

- ganeshie8

opposite of
"all of them are green"
is
"not all of them are green"
which is same as
"at least one of them is not green"

- mathmath333

ohk

- ganeshie8

lets do couple more quick examples

- ganeshie8

whats the opposite of "at least one of my shirts is red"

- mathmath333

None of my shirts is red

- ganeshie8

good,
whats the opposite of "all of my shirts are blue"

- mathmath333

all of my shirts are not blue

- ganeshie8

do you mean : "there is at least one shirt that is not blue" ?

- mathmath333

ya this one

- ganeshie8

good
are you confident or want to do couple more ?

- mathmath333

confident

- ganeshie8

so from probability rules you must be knowing that
\[P(A) + P(A)' = 1\]

- mathmath333

yes

- ganeshie8

In our case,
\(P(A)\) : at least one of them is green
\(P(A)'\) : ?

- mathmath333

none of them is green

- ganeshie8

good, find its probability

- mathmath333

=1-(30C5)/(60C5)

- ganeshie8

Perfect!

- ganeshie8

that is correct, but could you explain how you got that ?

- mathmath333

p'(a)=1-p(a)
p(a)=none of them is green

- ganeshie8

looks good!

- ganeshie8

do you double check ur answer by working it using an alternative method ?

- mathmath333

as per probablity the chance of getting 1 from dice is 1/6
so is it true that if i threw a dice 6 times there will be 1 at least

- mathmath333

no i check by back of the book

- ganeshie8

probability is never "exactly" true

- ganeshie8

we say that seeing "1" at least once is more likely when you threw a dice 6 times

- ganeshie8

sometimes you might not get a single 1 even if you throw it 100 times
that can happen

- mathmath333

ok so its not true

- ganeshie8

yes, you can't use probability to win bets

- mathmath333

yep

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