## mathmath333 one year ago Probability question.

1. 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}}

2. ganeshie8

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

3. mathmath333

phi is a person , he is not a method

4. mathmath333

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

5. ganeshie8

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

6. ganeshie8

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

7. mathmath333

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

8. 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.

9. ganeshie8

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

10. mathmath333

ok my english / logic is weak.

11. ganeshie8

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

12. mathmath333

ok

13. ganeshie8

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

14. ganeshie8

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

15. mathmath333

none of them is green

16. ganeshie8

wrong

17. mathmath333

y

18. 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"

19. mathmath333

ohk

20. ganeshie8

lets do couple more quick examples

21. ganeshie8

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

22. mathmath333

None of my shirts is red

23. ganeshie8

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

24. mathmath333

all of my shirts are not blue

25. ganeshie8

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

26. mathmath333

ya this one

27. ganeshie8

good are you confident or want to do couple more ?

28. mathmath333

confident

29. ganeshie8

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

30. mathmath333

yes

31. ganeshie8

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

32. mathmath333

none of them is green

33. ganeshie8

good, find its probability

34. mathmath333

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

35. ganeshie8

Perfect!

36. ganeshie8

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

37. mathmath333

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

38. ganeshie8

looks good!

39. ganeshie8

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

40. 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

41. mathmath333

no i check by back of the book

42. ganeshie8

probability is never "exactly" true

43. ganeshie8

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

44. ganeshie8

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

45. mathmath333

ok so its not true

46. ganeshie8

yes, you can't use probability to win bets

47. mathmath333

yep