Historically, the likelihood for stock going up in a particular year is 53% - little better than a coin flip. According to Investopedia, there seems a January Effect in the stock market. If there is a January rally, then the probability that the market will have a good year is 60%. Statistics also shows that the probability of January rally is 62%.

1. What is the probability that there is a January rally followed by a good year?
2. If the yearly performance is in a positive territory, what is the probability that there was no January rally?
3. What is the probability of encountering a bear market in both January and the whole year?
4. Are the two events "January rally" and "Good year" independent? mutually exclusive? Why?