Assume that in any given month, the probability of a positive return on the stock market is exactly 50%. A financial adviser sends you at the end of every month a promotional email recommending either a long or a short position on the market for the next month.

1. You receive correct recommendations for 6 months in a row. What is the probability of this happening purely due to chance? (I.e. what is the p-value for a test of the null hypothesis: H0 : The adviser can not predict markets.) 
2. The adviser sends each month promotional emails to 100.000 receivers. Each month, the adviser randomly selects 50.000 receivers who get the recommendation to go long, while the other 50.000 get the recommendation to go short. After 6 months, how many people are expected to have received six correct recommendations in a row?