mathmath333
  • mathmath333
Probability question.
Mathematics
jamiebookeater
  • jamiebookeater
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mathmath333
  • 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
  • ganeshie8
may be work the probability for "none will be green" then subtract that from 1
mathmath333
  • mathmath333
phi is a person , he is not a method

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mathmath333
  • mathmath333
but substracting from (1- "none will be green") Will resemble all will be green
ganeshie8
  • ganeshie8
whats the negation of "none of them are green" ?
ganeshie8
  • ganeshie8
do you say "none of them are green" to below set ? {B R B R G B} ?
mathmath333
  • mathmath333
All will be green ? Or At least one will be green . i am confused
mathmath333
  • 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
  • ganeshie8
negation of "none of them are green" is "at least one of them is green"
mathmath333
  • mathmath333
ok my english / logic is weak.
ganeshie8
  • ganeshie8
your english/logic is fine, it takes some to see why above is true lets do some examples may be
mathmath333
  • mathmath333
ok
ganeshie8
  • ganeshie8
whats the opposite of statement : "all of them are green"
ganeshie8
  • ganeshie8
whats the opposite of statement : "all of them did good"
mathmath333
  • mathmath333
none of them is green
ganeshie8
  • ganeshie8
wrong
mathmath333
  • mathmath333
y
ganeshie8
  • 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
  • mathmath333
ohk
ganeshie8
  • ganeshie8
lets do couple more quick examples
ganeshie8
  • ganeshie8
whats the opposite of "at least one of my shirts is red"
mathmath333
  • mathmath333
None of my shirts is red
ganeshie8
  • ganeshie8
good, whats the opposite of "all of my shirts are blue"
mathmath333
  • mathmath333
all of my shirts are not blue
ganeshie8
  • ganeshie8
do you mean : "there is at least one shirt that is not blue" ?
mathmath333
  • mathmath333
ya this one
ganeshie8
  • ganeshie8
good are you confident or want to do couple more ?
mathmath333
  • mathmath333
confident
ganeshie8
  • ganeshie8
so from probability rules you must be knowing that \[P(A) + P(A)' = 1\]
mathmath333
  • mathmath333
yes
ganeshie8
  • ganeshie8
In our case, \(P(A)\) : at least one of them is green \(P(A)'\) : ?
mathmath333
  • mathmath333
none of them is green
ganeshie8
  • ganeshie8
good, find its probability
mathmath333
  • mathmath333
=1-(30C5)/(60C5)
ganeshie8
  • ganeshie8
Perfect!
ganeshie8
  • ganeshie8
that is correct, but could you explain how you got that ?
mathmath333
  • mathmath333
p'(a)=1-p(a) p(a)=none of them is green
ganeshie8
  • ganeshie8
looks good!
ganeshie8
  • ganeshie8
do you double check ur answer by working it using an alternative method ?
mathmath333
  • 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
  • mathmath333
no i check by back of the book
ganeshie8
  • ganeshie8
probability is never "exactly" true
ganeshie8
  • ganeshie8
we say that seeing "1" at least once is more likely when you threw a dice 6 times
ganeshie8
  • ganeshie8
sometimes you might not get a single 1 even if you throw it 100 times that can happen
mathmath333
  • mathmath333
ok so its not true
ganeshie8
  • ganeshie8
yes, you can't use probability to win bets
mathmath333
  • mathmath333
yep

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