Question 67020: Grace has 16 jellybeans in her pocket. She has 8 red ones, 4 green ones, and 4 blue ones. What is the minimum number of jellybeans she must take out of her pocket to ensure that she has one of each color?
Found 2 solutions by venugopalramana, ikleyn:
Answer by venugopalramana(3286)   (Show Source):
You can put this solution on YOUR website! Grace has 16 jellybeans in her pocket. She has 8 red ones, 4 green ones, and 4 blue ones. What is the minimum number of jellybeans she must take out of her pocket to ensure that she has one of each color?
QUESTION IS NOT FRAMED PROPERLY...WE CAN NEVER BE SURE ON THIS FROM PROBABILITY
POINT OF VIEW.WE CAN ONLY SAY THAT IT IS SOME 60% OR 20% OR....ETC..PROBABLE.
IF WE TALK THEORETICALLY,
IF WE ARE LUCKY MINIMUM OF 3 SHOULD DO TO GET 3 DIFFERENT COLORS
AND IF WE ARE UNLUCKY MAXIMUM OF 8+4+1=13 ARE NEEDED TO GET ALL 3 COLORS.
SO WE MAY NEED ANY WHERE BETWEEN 3 TO 13 CHANCES TO GET ALL 3 COLOURS
BUT THEIR PROBABILITIES DIFFER.13 IS A CERTAINITY..100% PROBABLE
3 IS A RARE OCCURRENCE
Answer by ikleyn(54062)  (Show Source):
You can put this solution on YOUR website! .
Grace has 16 jellybeans in her pocket. She has 8 red ones, 4 green ones, and 4 blue ones.
What is the minimum number of jellybeans she must take out of her pocket to ensure that she has one of each color?
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Another tutor hesitates, does not know how to start, and instills hesitation in the reader.
Meanwhile, this is a standard problem. It is correctly formulated and has a standard solution —
one that you should know and solve without any hesitation.
In the worst case, Grace takes 8 red jellybeans and 4 green jellybeans, totaling 8+4 = 12 jellybeans,
but still does not have one of each color.
In another worst case, Grace takes 8 red jellybeans and 4 blue jellybeans, totaling 8+4 = 12 jellybeans,
but still does not have one of each color.
But in either of these two worst cases, as soon as Grace takes the next, 13th jellybean,
she will have one of each color.
Thus, the minimum number of jellybeans she must take out of her pocket to ensure that she has one of each color
is 13. ANSWER
At this point, the problem is solved completely.
You can meet many other similar problems. Usually, they are of the same type and admit a similar solution.
Start thinking about the worst case - usually it is a key to the solution that works.
| |
|
