Volatile Yard 挥洒自如 Write anything I want to write...

I don't like to eat meats since I was a kid as I really don't like their taste, while my family members are ok with them. I vomited a few times trying to take meats. Wonder if this is fated? I recall an interesting incident many years ago that might probably tell.

One day, my family went to buy satay to eat together at home. We hardly had satay at home in my hometown, and this is in fact the only time I also ate together as I can remember. (I just enjoy chewing the satay but not really its taste. Odd huh?) Something interesting then happened. Well, you normally will not find any bone from satay, unless the hawker had missed it accidentally. Now the incident:

We bought 20 satay sticks altogether. I took 4 sticks to eat, and I found real 'genuine' chicken bones (later examined by my family members too) in 3 out of that 4 sticks! While they didn't find any bone in other sticks! I swear that I did not choose them purposely as I didn't see the bones before I eat them. I treat it as a sign that I was fated to be discouraged from taking meats, ha... So now the mathematical questions:

• There are 20 satay sticks, and bones are found in 3 of them. What is the probability that, when you choose 4 of them randomly, you picked up the 3 sticks with bone?
• Given the same scenario, what is the probability if you choose only 3 of them randomly but happened to picked up all the 3 sticks with bone? (I might have picked those 3 too if I only choose 3 of them. Unfortunately this cannot be verified now.)

Check below for the solution. Think first if you can!

Solution

The second question is in fact easier, so let's solve it first. There are ₂₀C₃ ways to choose 3 from 20 sticks, and only one of them results in having 3 sticks with bones being chosen. So the probability is 1 / ₂₀C₃ = 1 / ((20x19x18)/(3x2x1)) = 6 / 6840 = 1 / 1140 = 0.0877%. So the chance is low!

Now come back to the first question. There are ₂₀C₄ ways to choose 4 from 20 sticks. For the 4 sticks chosen: The 3 sticks with bones must be chosen and there is only one way to do it; There are 17 ways to choose the remaining stick since there are 17 sticks without bone. So the probability is 1x17 / ₂₀C₄ = 17 / ((20x19x18x17)/(4x3x2x1)) = 1 / 285 = 0.3509%.

See, mathematics is useful for telling your fate, and it is not that difficult if you concept is clear, right?

So, 1 out of either 1140 or 285, not very deeply fated, but still fated. Ha! Anyway, I like vegetables and like the way I eat now. I eat more vegetables and less meats as I grow up. Eat more vegetables, be more environmental (see this and this [en.wikipedia.org]), be healthier, and save the Earth!