Probability Tes...

A coin is tossed $$40$$ times and it showed tail $$24$$ times.The probability of getting a head was:

A, B are two inaccurate arithmeticians whose chances of solving a given question correctly are (1/8) and (1/12) respectively. They solve a problem and obtained the same result. If it is 1000 to 1 against their making the same mistake, find the chance that the result is correct

In a test, an examine either guesses or copies or knows the answer to a  multiple choice question with four choices. The probability that he makes a guess is $$\displaystyle \frac { 1 }{ 3 } $$ and the probability that he copies the answer is $$\displaystyle \frac { 1 }{ 6 } $$. The probability that his answer is correct given that he copied it is $$\displaystyle \frac { 1 }{ 8 }$$. The probability that he knew the answer to the question given that he correctly answered it, is 

Suppose that of all used cars of a particular year 30% have bad brakes. You are considering buying a used car of that year. You take the car to a mechanic to have the brakes checked. The chance that the mechanic will give you the wrong report is 20%. Assuming that the car you take to the mechanic is selected at random from the population of cars of that year. The chance that the car's brakes are good, given that the mechanic says its brakes are good, is

If $$E$$ and $$F$$ are independent events such that $$P(E) = 0.7$$ and $$P(F) = 0.3$$, then P$$\displaystyle (E\cap F)$$

A pack of cards was found to contain only $$51\ cards$$. If first $$13\ cards$$, which are examined, are all red, then find the probability that the missing cards is black?

A box has four dice in it. Three of them are fair dice but the fourth one has the number five on all of its faces. A die is chosen at random from the box and is rolled three times and shows up the face five on all the three occasions. The chance that the die chosen was a rigged die, is

In a simultaneous throw of two dice, what is the number of exhaustive events?

In figure points A, B, C and D are the centre of four circles that each have a radius of length one unit. If a point is selected at random from the interior of square ABCD. What is the probability that the point will be chosen from the shaded region?

A & B are sharp shooters whose probabilities of hitting a target are $$\displaystyle \frac{9}{10}$$ & $$\displaystyle \frac{14}{15}$$ respectively. If it is knownthat exactly one of them has hit the target, then the probability that it was hit by A is equal to