Probability Tes...

A throws a coin $$3$$ times. If he get a head all three times, he is to get a reward of Rs.$$200$$, on the other hand if he does not get $$3$$ heads he is to loose Rs.40. He is expected to win Rs. ...............

If $$\displaystyle P(A) = \frac{2}{3}$$, $$\displaystyle P(B) = \frac{4}{9}$$ and $$\displaystyle P(A \cap B) = \frac{14}{45}$$ then $$\displaystyle P(A' \cap B') $$ is greater than or equal to

The percentage of marks obtained by a student in the monthly unit tests are given.

Let $${E}^{e}$$ denotes the complement of an event $$E$$. If $$E,F,G$$ are pairwise independent events with $$P(G)> 0$$ and $$P(E\cap F\cap G)=0$$. Then, $$P({ E }^{ e }\cap { F }^{ e }|G)$$ equals

The probability that $$A$$ can solve a problem is $$\dfrac {2 }{ 3}$$ and that $$B$$ can solve is $$\dfrac {3 }{4}$$. If both of them attempt the problem. What is probability that the problem act solved?

If the probability for A to fail in an examination is 0.8 and that for B is 0.7 , then the probability that atleast one of A or B fails, is 

Let $$A,\ B,\ C$$ be pairwise independent even such that $$P(C)> 0$$ and $$P(A\cap B\cap C)=0$$, then $$P(A'\cap B'\cap C)$$ is equal to  

Two numbers $$b$$ and $$c$$ are chosen at random with replacement from the numbers $$1,\,2,\,3,\,4,\,5,\,6,\,7,\,8$$ and $$9$$.The probability that $${x}^{2}+bx+c>0$$ for all $$x\in R$$ is

If $$A$$ and $$B$$ are two independent events such that $$P(A)=\dfrac{1}{3}$$ and $$P(B)=\dfrac{3}{4}$$, then $$p\left\{\dfrac{B}{(A\cup B)}\right\}$$

If A and B are two events such that P (A)=$$\frac{1}{2}$$ and P (B) = $$\frac{2}{3}$$ , then which of the