Problem A
I have tried to give probabilities for the success of each choice based on what the cards the opps are likely to hold and also what the opps would do. Here are my thoughts:
We know that East does not have a 5 card major suit and very likely does not have 4-4 in the majors either since East would Stayman with 4441 and quite likely 4432 no matter what strength since a 4-4 fit is odds on and this is match points. East’s most likely distributions are therefore 3451 or 3442 and West 4432 giving partner 4441. Strength wise there are 10HCP to share between partner and East and so 5 each is most likely.
You bid 3♣.
East with 3451distribution would likely double with 5+HCP if so EW would almost certainly get a positive score. With equal or fewer than 5HCP EW are unlikely to double. Probable scores: 50% -140 (opps double), 50% +110.
You pass
Everything hinges on what partner leads. Given that a club lead, in order not to give away a trick, looks very low probability, then there is a 33% chance of finding the killing ♥ lead. A pointy suit lead looks like giving the opps 7 or 8 tricks. Possible scores: 33% +300; 67% -100 or -200.
You bid 3NT
If west has ♠AK or ♦AK then he will lead it. If partner does not have the A in the other suit, then we score anything between -100 and -400. (Exception is when partner has Q over AK and QJ in the other suit). What is the likelihood of having ♠AK or ♦AK? I would reckon about 50%. Given that chance, what are the odds of partner having the A of the other suit or the magic Q and QJ stop? 30% perhaps?
The other 50% of the time when west does not have ♠AK or ♦AK, what is the chance of a ♥ lead? Picking 1 out of 3 suits it would be 33%. The remaining 67% chance of leading ♥ or ♠ there is still a chance of making if partner has an ace. I would rate this chance to be about 20%. Chance of making with this 50% = 0.33 + 0.67*0.2 = 0.46.
Overall chance of making 3N = (0.46+0.3)/2 = 38%
Reward /Risk ratio
Pass is low risk low reward
3♣ is low risk moderate reward
3N is moderate to high risk and high reward.
If we go for the best chance of a positive score the 3♣ looks best.
Probability 3♣ Pass 3NT
Positive score 50% 33% 38%
Conclusion
Choices are fairly close but based on this rough analysis I will go for 3♣
