You have a jar of jelly beans. There are 100 jelly beans in total, 10 of each of the following flavors, 10 banana, 10 strawberry, 10 apple, 10 grape, 10 cherry, 10 watermelon, 10 vanilla, 10 blueberry, 10 lime, 10 mango. How many jelly beans do you have to choose from the jar (without looking) to ENSURE that you have at LEAST 2 watermelon jelly beans?
2007-07-25 11:10:56 · 6 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
Well, worst case scenario is that you choose ALL of the beans of every other flavor before ever getting even 1 watermelon.
So you might pick 10 banana, 10 strawberry, 10 apple... and so on. After picking all 90 of these, you then choose 1 watermelon, followed by a second watermelon.
So at the very very worst, you might pick 92 jelly beans before getting 2 watermelon. Remember, it is unlikely to take that long, but you will be guaranteed two watermelons if you choose 92 beans.
On the other hand, if you just wanted 2 of any flavor, you might pick 1 of each of the 10 flavors, and then no matter what, your 11th will be a repeat. Much quicker!
2007-07-25 11:17:49 · answer #1 · answered by T F 4 · 0⤊ 0⤋
This falls into the "pigeon-hole" category of problems. Basically, you assume the worst-case scenario, in which you draw all the non-watermelon jelly beans first.
So, you draw 90 non-watermelon jelly beans. Now, the only jelly beans left are watermelon. So, the next two beans you select must be watermelon, which fulfills the requirement.
Therefore, you must draw 92 jelly beans to completely guarantee you get at least 2 watermelon-flavored beans.
2007-07-25 18:15:04 · answer #2 · answered by lithiumdeuteride 7 · 1⤊ 1⤋
Uhhh...92 I think. Because you could choose 10 of all the others first before you get to the watermelon jelly beans.
That's my logic anyway - for what it's worth.
2007-07-25 18:15:31 · answer #3 · answered by Anonymous · 1⤊ 1⤋
92.
You could potentially pick all 90 of the other flavors, then two watermelon.
2007-07-25 18:14:37 · answer #4 · answered by Deborah P 2 · 2⤊ 0⤋
Well, you have to think of the worst case scenario. Say you picked all the beans of all the other flavors first, and add 2 to that.
2007-07-25 18:14:14 · answer #5 · answered by Handsome Chuck 5 · 1⤊ 1⤋
92
You could get all 10 of every other flavor and then there would be all watermelon left
2007-07-25 18:38:46 · answer #6 · answered by Traci 2 · 0⤊ 1⤋