Probability Tes...

If $$A$$ and $$B$$ are two events such that $$P(A \cup B) = \dfrac {3}{4}. P(A\cap B) = \dfrac {1}{4}$$ and $$P(\overline {A}) = \dfrac {2}{3}$$, then what is $$P(B)$$ equal to?

Simone and her three friends were deciding how to pick the song they will sing for their school's talent show. They decide to roll a number cube.
The person with the lowest number chooses the song. If her friends rolled a 6, 5, and 2, what is the probability that Simone will get to choose the song?

There are $$n$$ persons sitting in a row. Two of them are selected at random. The probability that the two selected persons are not together, is

The probability that a man will live $$10$$ more years, is $$\dfrac { 1 }{ 4 }$$ and the probability that his wife will live $$10$$ more years, is $$\dfrac { 1 }{ 3 }$$. Then, what is the probability that neither will be alive in $$10$$ years?

A coin is tossed three times. Consider the following events:
A: No head appears
B: Exactly one head appears
C: At least two heads appear
Which one of the following is correct?

From $$50$$ students taking examinations in Mathematics, Physics and Chemistry, $$37$$ passed in Mathematics, $$24$$ in Physics and $$43$$ in Chemistry. Atmost $$19$$ passed in Mathematics and Physics, atmost $$29$$ passed in Mathematics and Chemistry and atmost $$20$$ passed in Physics and Chemistry. The largest possible number that could have passed all three examination, is?

A purse contains $$4$$ copper coins and $$3$$ silver coins. A second purse contains $$6$$ copper coins and $$4$$ silver coins. A purse is chosen randomly and a coin is taken out of it. What is the probability that it is a copper coin?

Two events A and B are such that $$P($$not $$B)$$ $$= 0.8$$, $$P(A\cup B)=0.5$$ and $$P(A\setminus B)=0.4$$ Then $$P(A)$$ is equal to 

Probability of solving a particular question by person $$A$$ is $$\dfrac { 1 }{ 3 }$$ and probability of solving that question by person $$B$$ is $$\dfrac { 2 }{ 5 } $$. What is the probability of solving that question by atleast one of them?

A box contains $$6$$ green balls, $$4$$ blue balls and $$5$$ yellow balls. A ball is drawn at random. Find the probability of
(a) Getting a yellow ball.
(b) Not getting a green ball.