A farmer has a rose garden. Every day he either plucks 7 or 6 or 24 or 23 roses. The rose plants are intelligent and when the farmer plucks these no. of roses, the next day 37 or 36 or 9 or 18 new rose bloom up in the garden respectively. On Monday he counts 189 roses, he plucks the roses as per his plan on consecutive days and new roses bloom up as per the intelligence of the plants mentioned above. After some days which of the following can be the number of roses in the garden?
Robin and Williams are playing a game. An
unbiased coin is tossed repeatedly. Robin wins as soon as the sequence
of tosses HHT appears. Williams wins as soon as the sequence of tosses
HTH appears. The game ends when one of them wins. What are the
probabilities of winning for each player?