The Mathematics of Maybe : Introduction to Probability — Important Questions

3/4

The sample space is {HH, HT, TH, TT}. At least one head occurs in HH, HT, and TH. So favourable outcomes = 3 and total outcomes = 4. Probability = 3/4.

2/11

The word PROBABILITY has 11 letters and 2 of them are B. So, probability = 2/11 ≈ 0.182 or 18.2%.

It is an example of Gambler's Fallacy, The next roll is still an independent event, A fair die has no memory of past rolls

This belief is wrong because each roll of a fair die is independent. The die has no memory, so the chance of getting 6 remains 1/6 on the next roll.

The sample space is {HH, HT, TH, TT}, The event of getting exactly one head is {HT, TH}, An event is a subset of a sample space

For two coin tosses, the sample space has 4 outcomes: {HH, HT, TH, TT}. Exactly one head occurs in HT and TH. An event is a subset of the sample space.