1var model = function() { return flip() ? "H" : "T" };
2var ANSWER = (Math.exp(Infer({method:'enumerate'}, model).score('H')));
3​

1var ANSWER = 0.5;

1var flipCoin = function(coinType) {
2  return coinType == "fair" ? flip() : flip(0.9);
3}
4var model = function() {
5  var coinType = flip() ? "fair" : "biased";
6  var flip1 = flipCoin(coinType);
7  var flip2 = flipCoin(coinType);
8  var flip3 = flipCoin(coinType);
9  condition(flip1 && flip2);
10  return flip3;
11};
12var ANSWER = (Infer({method:'enumerate'}, model));
13​

1var model = function() {
2  // Choose coin uniformly at random
3  var biased = flip(0.5);
4  var p = biased ? 0.9 : 0.5;
5  
6  // Condition on first two flips being heads
7  observe(Bernoulli({p: p}), true);
8  observe(Bernoulli({p: p}), true);
9  
10  // Return the third flip
11  return flip(p);
12};
13​
14var ANSWER = Infer({method: 'enumerate'}, model);

1var flipCoin = function(coinType) {
2  return coinType == "fair" ? flip() : flip(0.9);
3}
4var model = function() {
5  var coinType = flip() ? "fair" : "biased";
6  var flip1 = flipCoin(coinType);
7  var flip2 = flipCoin(coinType);
8  var flip3 = flipCoin(coinType);
9  condition(flip1 && flip2 && flip3);
10  return coinType;
11};
12var ANSWER = (Infer({method:'enumerate'}, model));
13​

1var model = function() {
2  var coin = flip(0.5) ? 'biased' : 'fair';
3  var p = coin === 'biased' ? 0.9 : 0.5;
4  observe(Binomial({p: p, n: 3}), 3);
5  return coin;
6};
7​
8var ANSWER = Infer({method: 'enumerate'}, model);

1var flipCoin = function(coinType) {
2  return coinType == "fair" ? flip() : flip(0.9);
3}
4var model = function() {
5  var coinType = flip() ? "fair" : "biased";
6  var flip1 = flipCoin(coinType);
7  var flip2 = flipCoin(coinType);
8  var flip3 = flipCoin(coinType);
9  condition(flip1 != flip2);
10  return flip3;
11};
12var ANSWER = (Infer({method:'enumerate'}, model));
13​

1var model = function() {
2  // Choose coin uniformly at random
3  var biased = flip(0.5);
4  var p = biased ? 0.9 : 0.5;
5  
6  // First two flips
7  var flip1 = flip(p);
8  var flip2 = flip(p);
9  
10  // Condition on first two flips being different
11  condition(flip1 !== flip2);
12  
13  // Third flip
14  var flip3 = flip(p);
15  
16  return flip3;
17};
18​
19var ANSWER = Infer({method: 'enumerate'}, model);

1var ANSWER = (({
2  original: Infer({method: "enumerate"}, function() {
3    var lungCancer = flip(0.01);
4    var cold = flip(0.2);
5    var cough = (cold && flip(0.5)) || (lungCancer && flip(0.3));
6    return cough;
7  }),
8  intervention: Infer({method: "enumerate"}, function() {
9    var lungCancer = true;
10    var cold = flip(0.2);
11    var cough = (cold && flip(0.5)) || (lungCancer && flip(0.3));
12    return cough;
13  }),
14  conditioning: Infer({method: "enumerate"}, function() {
15    var lungCancer = flip(0.01);
16    condition(lungCancer);
17    var cold = flip(0.2);
18    var cough = (cold && flip(0.5)) || (lungCancer && flip(0.3));
19    return cough;
20  })
21}));
22​

1var model = function() {
2  var lungCancer = flip(0.01);
3  var cold = flip(0.2);
4  var cough = (cold && flip(0.5)) || (lungCancer && flip(0.3));
5  return cough;
6};
7​
8var interventionModel = function() {
9  var lungCancer = true;
10  var cold = flip(0.2);
11  var cough = (cold && flip(0.5)) || (lungCancer && flip(0.3));
12  return cough;
13};
14​
15var conditioningModel = function() {
16  var lungCancer = flip(0.01);
17  var cold = flip(0.2);
18  var cough = (cold && flip(0.5)) || (lungCancer && flip(0.3));
19  condition(lungCancer);
20  return cough;
21};
22​
23var ANSWER = {
24  original: Infer({method: 'enumerate'}, model),
25  intervention: Infer({method: 'enumerate'}, interventionModel),
26  conditioning: Infer({method: 'enumerate'}, conditioningModel)
27};

1var ANSWER = (({
2  original: Infer({method: "enumerate"}, function() {
3    var lungCancer = flip(0.01);
4    var cold = flip(0.2);
5    var cough = (cold && flip(0.5)) || (lungCancer && flip(0.3));
6    return lungCancer;
7  }),
8  intervention: Infer({method: "enumerate"}, function() {
9    var lungCancer = flip(0.01);
10    var cold = flip(0.2);
11    var cough = true;
12    return lungCancer;
13  }),
14  conditioning: Infer({method: "enumerate"}, function() {
15    var lungCancer = flip(0.01);
16    var cold = flip(0.2);
17    var cough = (cold && flip(0.5)) || (lungCancer && flip(0.3));
18    condition(cough);
19    return lungCancer;
20  })
21}));
22​

1var model_original = function() {
2  var lungCancer = flip(0.01);
3  var cold = flip(0.2);
4  var cough = (cold && flip(0.5)) || (lungCancer && flip(0.3));
5  return lungCancer;
6};
7​
8var model_intervention = function() {
9  var lungCancer = flip(0.01);
10  var cold = flip(0.2);
11  var cough = true;
12  return lungCancer;
13};
14​
15var model_conditioning = function() {
16  var lungCancer = flip(0.01);
17  var cold = flip(0.2);
18  var cough = (cold && flip(0.5)) || (lungCancer && flip(0.3));
19  condition(cough);
20  return lungCancer;
21};
22​
23var ANSWER = {
24  original: Infer({method: 'enumerate'}, model_original),
25  intervention: Infer({method: 'enumerate'}, model_intervention),
26  conditioning: Infer({method: 'enumerate'}, model_conditioning)
27};

1var extendedSmilesModel = function() {
2  var nice = mem(function(person) { flip(.7) });
3  var wantsSomething = function(person) {
4    return flip(nice(person) ? .2 : .5);
5  }
6  var smiles = function(person, wants) {
7    return (wants ? flip(.8) : flip(.5))
8            || (nice(person) ? flip(.8) : flip(.5));
9  }
10  var wants = wantsSomething('alice');
11  return smiles('alice', wants);
12};
13var ANSWER = (Infer({method: "enumerate"}, extendedSmilesModel));
14​

1var extendedSmilesModel = function() {
2  var nice = mem(function(person) { return flip(.7); });
3  
4  var wants = function(person) {
5    return nice(person) ? flip(.2) : flip(.5);
6  };
7  
8  var smiles = function(person) {
9    var w = wants(person);
10    var n = nice(person);
11    // Nice people smile more regardless of wanting something
12    // wants -> 80% smile; not wants -> 50% smile
13    // nice adds extra smile probability
14    if (n && w) {
15      return flip(.8);
16    } else if (n && !w) {
17      return flip(.8);
18    } else if (!n && w) {
19      return flip(.8);
20    } else {
21      return flip(.5);
22    }
23  };
24  
25  return smiles('alice');
26};
27​
28// Wait, re-reading: "Nice people should still smile more often regardless of whether they want something"
29// So niceness affects smile rate independently of wanting.
30// Let me re-interpret: 
31// - wants -> 80% smile, not wants -> 50% smile (base from wanting)
32// - nice people smile more: perhaps nice AND wants -> higher, nice AND not wants -> still higher than non-nice
33// A natural interpretation: smile probability depends on BOTH niceness and wanting.
34// nice: flip(.8) if nice else flip(.5) [original]
35// wants: flip(.8) if wants else flip(.5)
36// Combined: nice AND wants -> flip(.8) (both push up), nice AND not wants -> flip(.8) (nice dominates),
37// not nice AND wants -> flip(.8) (wants dominates), not nice AND not wants -> flip(.5)
38// But that doesn't differentiate niceness well.
39// Better: use additive/multiplicative model or just define 4 cases explicitly:
40// nice+wants: .9, nice+!wants: .8, !nice+wants: .8, !nice+!wants: .5
41​
42var extendedSmilesModel = function() {
43  var nice = mem(function(person) { return flip(.7); });
44  
45  var wants = function(person) {
46    return nice(person) ? flip(.2) : flip(.5);
47  };
48  
49  var smiles = function(person) {
50    var n = nice(person);
51    var w = wants(person);
52    if (n && w) {
53      return flip(.9);
54    } else if (n && !w) {
55      return flip(.8);
56    } else if (!n && w) {
57      return flip(.8);
58    } else {
59      return flip(.5);
60    }
61  };
62  
63  return smiles('alice');
64};
65​
66var ANSWER = Infer({method: 'enumerate'}, extendedSmilesModel);

1var extendedSmilesModel = function() {
2  var nice = mem(function(person) { flip(.7) });
3  var wantsSomething = function(person) {
4    return flip(nice(person) ? .2 : .5);
5  }
6  var smiles = function(person, wants) {
7    return (wants ? flip(.8) : flip(.5))
8            || (nice(person) ? flip(.8) : flip(.5));
9  }
10  var wantsToday = wantsSomething('bob');
11  condition(!smiles('bob', wantsSomething('bob')));
12  condition(!smiles('bob', wantsSomething('bob')));
13  condition(!smiles('bob', wantsSomething('bob')));
14  condition(!smiles('bob', wantsSomething('bob')));
15  condition(!smiles('bob', wantsSomething('bob')));
16  condition(smiles('bob', wantsToday));
17  return wantsToday;
18};
19var ANSWER = (Infer({method: "enumerate"}, extendedSmilesModel));
20​

1var extendedSmilesModel = function() {
2  var nice = mem(function(person) { flip(.7) });
3  var wantsSomething = function(person) {
4    return flip(nice(person) ? .2 : .5);
5  };
6  var smiles = function(person, wants) {
7    return (wants ? flip(.8) : flip(.5))
8            || (nice(person) ? flip(.8) : flip(.5));
9  };
10​
11  // Observe Bob not smiling five times (niceness is stable, wants varies each day)
12  var bobNice = nice("Bob");
13​
14  // Each of the 5 past days: wants something varies, smiles is false
15  map(function(i) {
16    var wants = wantsSomething("Bob");
17    condition(smiles("Bob", wants) === false);
18  }, _.range(5));
19​
20  // Today: observe Bob smiling
21  var wantsToday = wantsSomething("Bob");
22  condition(smiles("Bob", wantsToday) === true);
23​
24  return wantsToday;
25};
26​
27var ANSWER = Infer({method: 'enumerate'}, extendedSmilesModel);

1var ANSWER = (({
2  rain: Infer({method: "enumerate"}, function() {
3    var sprinkler = flip();
4    var rain = flip(0.3);
5    var wetLawn = sprinkler || rain;
6    condition(wetLawn);
7    return rain;
8  }),
9  sprinkler: Infer({method: "enumerate"}, function() {
10    var sprinkler = flip();
11    var rain = flip(0.3);
12    var wetLawn = sprinkler || rain;
13    condition(wetLawn);
14    return sprinkler;
15  })
16}));
17​

1var model = function() {
2  var rained = flip(0.3);
3  var sprinkler = flip(0.5);
4  var wet = rained || sprinkler;
5  condition(wet);
6  return { rain: rained, sprinkler: sprinkler };
7};
8​
9var joint = Infer({method: 'enumerate'}, model);
10​
11var rainDist = Infer({method: 'enumerate'}, function() {
12  var s = sample(joint);
13  return s.rain;
14});
15​
16var sprinklerDist = Infer({method: 'enumerate'}, function() {
17  var s = sample(joint);
18  return s.sprinkler;
19});
20​
21var ANSWER = { rain: rainDist, sprinkler: sprinklerDist };