Probability Tes...

If $$P(E_k)=C$$ for $$0\leq k\leq n$$, then $$P(A)$$ equals

A box contain $$N$$ coins, $$m$$ of which are fair are rest and biased. The probability of getting a head when a fair coin is tossed is $$1/2$$, while it is $$2/3$$ when a biased coin is tossed. A coin is drawn from the box at random and is tossed twice. The first time it shows head and the second time it shows tail. The probability that the coin drawn is fair is

A player throws a fair cubical die and score the number appearing on the die. If he throws a $$1$$, he gets a further throw. Let $$p_r$$ denote the probability of getting a total score of exactly $$r$$. Sum of the series $$\displaystyle S=\sum_{r=1}^{\infty}p_r$$ is

A bag contains $$(2n+1)$$ coins. It is known that $$n$$ of these coins have a head on both sides, whereas the remaining $$n+1$$ coins are fair. A coin is picked up at random from the bag and tossed. If the probability that the toss results in a head is $$\displaystyle \frac{31}{42}$$, then $$n$$ is equal to 

The probability that certain electronic component fails when first used is $$0.10.$$ If it does not fail immediately, the probability that is lasts for one year is $$0.99.$$ The probability that a new component will last for one year is

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

Let $$p$$ be the probability that a man aged $$x$$ years will die in a year time. The probability that out of $$n$$ men $$\displaystyle A_{1},A_{2},A_{3},....,A_{n}$$ each aged $$x$$ years, $$\displaystyle A_{1}$$ will die & will be the first to die, is

A random variable $$X$$ has the probability distribution

A fair coin is tossed $$99$$ times. If X is the number of times heads occur then P(X = r) is maximum when r is

A purse contains $$2$$ six-sided dice. One is a normal fair die,while the other has two $$1's, $$ two $$ 3' s$$ and two $$5'$$, A die is picked up and rolled. Because of some secret magnetic attration of the unfair die, there is 75% chance of picking the unfair die and a 25% chance of picking a fair die. The die is rolled and shows up the face $$3$$ The probability that a fair die was picked up is