I am not sure if this is the right place for you to ask this kind of question, unless you were asking how to calculate it using SAS, which in that case, I can't provide the answer. That being said, you may get better answers(academic wise) elsewhere.
Q1.
When you say 'chance', I would reflect 'probability', which will never larger than 1 (I hope I am not too statistical anal here). Anyway, to anwer your question:
If you throw 3 times, then the total number of possible senario will be: 2(head,tail)*2*2=8
And the total number of 2-heads secario: 3*2/2=3, sorry don't know how to post the formula symbol.
Therefore the chance of your getting 2-heads is 3/8.
Q2.
Can't believe they ask that in an interview. Anyway, the maxium time you need to weigh is 3. here is how:
Rondomly you picked 4 balls, one pair on each side of balance:
pair A vs. Pair B,
1. if they don't balance, then choose the lighter pair do another weighing, then you get your answer. This is the better scenario, which only takes 2 times.
2. if they do balance, then put them aside, choose another 2 pairs from remaining 5 balls, and weight
2.1 if they do balance, then you will know the unweighed left one is the culprit. 2 times.
2.2 if they don't balance, then it will take you another weighing to decide. This is the worst scenario, and it takes 3 times.
Regards,
Haikuo
