What is the probability that at least two persons out of a group of three persons were born in the same month (disregard year) ?

If $$P(B) = {3 \over 4}$$, $$P(A \cap B \cap \overline C ) = {1 \over 3}$$ and $$P(\overline A \cap B \cap \overline C ) = {1 \over 3}$$, then what is $$P(B \cap C)$$ equal to ?

In a multiple-choice test, an examinee either knows the correct answer with probability p, or guesses with probability 1 $$-$$ p. The probability of answering a question correctly is $${1 \over m}$$, if he or she merely guesses. If the examinee answers a question correctly, the probability that he or she really knows the answer is

Five sticks of length 1, 3, 5, 7 and 9 feet are given. Three of these sticks are selected at random. What is the probability that the selected sticks can form a triangle?