Probability Tes...

In two mutually exclusive events of $$ P (A\cup B) $$is

Two events $$A$$ and $$B$$ are said to be mutually independent, if:

An event X can take place in conjunction with any one of the mutually exclusive and exhaustive events A, B and C. If A, B,C are equiprobable and the probability of X is 5/12 and the probability of X taking place when A has happened is 3/8 while it is 1/4 when B has taken place, then the probability of X taking place on conjunction with C is

For three events $$A,B$$ and $$C,P($$exactly one of the events $$A$$ or $$B$$ occurs$$)=P($$exactly one of the vents $$B$$ or $$C$$ occurs$$)=P($$exactly one of the events $$C$$ or $$A$$ occurs$$)=p$$ and $$P($$all the three events occur simultaneously$$)={ p }^{ 2 }$$, where $$\displaystyle 0<p<\frac { 1 }{ 2 } $$.
Then the probability of atleast one of the three events $$A,B$$ and $$C$$ occurring is

$$A, B$$ and $$\mathrm{C}$$ are three events such that $$P(\mathrm{A})=0.3, P(B)=0.4, P(C)=0.8$$,$$P(\mathrm{A}\cap B)=0.12, P(\mathrm{A}\cap C)=0.28$$, $$P(A\cap B\cap C)=0.09$$ and $$P(A\cup B\cup C)\geq 0.75$$, then the limits of $$P(B\cap C)$$ are

5 cards are drawn at random from a well shuffled pack of 52 playing cards. If it is known that there will be at least 3 hearts, the probability that all the 5 are hearts is

For the three events $$A, B$$ and $$C,$$ $$P$$(exactly one of the events $$A$$ or $$B$$ occurs) $$= P$$(exactly one of the events $$C$$ or $$A$$ occurs) $$= P$$(exactly one of the events $$B$$ or $$C$$ occurs) $$= p$$ and $$P$$( all three events occur simultaneously) = $$p^2$$, where $$0<p<\displaystyle\frac{1}{2}$$. Then find the probability of atleast one of the three events $$A, B$$ and $$C$$ occurring.

The odds that a book will be reviewed favourably by three independent critics are 5 to 2, 4 to 3 and 3 to 4 respectively. The probability that of the three reviewers a majority will be favourable

A pair of unbiased dice is rolled together till a sum is either $$5$$ or $$7$$ is obtained, The probability that $$5$$ comes before $$ 7$$ is

A student takes his examination in four subjects $$\alpha ,\beta ,\gamma ,\delta $$. He estimates his chance of passing in $$\alpha$$ is $$\displaystyle\frac{ 4 }{ 5 } $$, in $$\beta$$ is $$\displaystyle \frac { 3 }{ 4 } $$, in $$\gamma$$ is $$\displaystyle\frac { 5 }{ 6 } $$ and in $$\delta$$ is $$\displaystyle \frac { 2 }{ 3 }$$. The probability that he qualifies (passes in atleast three subjects) is