Probability Tes...

A certain player, say $$X$$, known to win with probability $$0.3$$ if the track is fast and $$0.4$$ if the track is slow. For Monday, there is a $$0.7$$ probability of a fast track and $$0.3$$ probability of a slow track. The probability that player $$X$$ will win a Monday, is

A letter is known to have come eithe from London or Clifton; on the post only the consecutive letters ON are legible; what is the chance that it came from London?

A sample of size $$4$$ is drawn with replacement be the first part of the problem and without replacement be the second part of the problem, then from an urn containing $$12$$ balls, of which $$8$$ are white, what is the conditional probability that the ball drawn on the third draw was white, given that the sample contains $$3$$ white balls ?

A person is know to speak the truth 4 times out of 5. He throws a die and reports that it is a ace. The probability that it is actually a ace is

Mr. Dupont is a professional wine taster. When given a French wine, he will identify it with probability $$0.9$$ correctly as French and will mistake it for a Californian wine with probability $$0.1$$. When given a Californian wine, he will identify it with probability $$0.8$$ correctly as Californian and will mistake it for a French wine with probability  $$0.2$$. Suppose that Mr. Dupont is given ten unlabelled glasses of wine, three with French and seven with Californian wines. He randomly picks a glass, tries the wine and solemnly says : "French". The probability that the wine he tasted was Californian, is nearly equal to

Twelve players $${ S }_{ 1 },{ S }_{ 2 },...,{ S }_{ 12 }$$ play in a chess tournament. They are divided into six pairs at random. From each pair a winner is decided. It is assumed that all players are of equal strength. The probability that both $${S}_{1}$$ and $${S}_{2}$$ are among the six winners is :

An artillery target may be either at point $$I$$ with the probability $$\displaystyle \frac { 8 }{ 9 } $$ or at the point $$II$$ with probability $$\displaystyle \frac { 1 }{ 9 } $$. We have $$21$$ shells each of which can be fired either at point $$I$$ or $$II$$. Each shell may hit the target independently of the other shell with probability $$\displaystyle \frac { 1 }{ 2 } $$. The number of shells which be fired at point $$I$$ to hit the target with maximum probability is 

If two events $$A$$ and $$B$$ are such that $$P(A')=0.3,P(B)=0.4$$ and $$P\left( A\cap B' \right) =0.5$$, then $$\displaystyle P\left( \frac { B }{ A\cup B' }  \right) $$ equala

The value of $$P(S \cap T)$$

A man is know to speak truth $$3$$ out of $$4$$ times. He throws a dice and reports that it is six. The probability that it is actually six is