Probability Tes...

If A and B are the two events of a sample space such that $$P(A\,\cup\,B)\, =\, \displaystyle \frac{5}{6}$$, $$P(A\,\cap\,B)\, =\,\displaystyle \frac{1}{3}$$, $$P(B)\, =\, \displaystyle \frac{1}{3}$$. Find P(A) 

If four positive integers are taken at random and multiplied together, then the probability that the last digit is 1, 3, 7 or 9 is

An investment consultant predicts that the odds against the price of a certain stock will go up during the next week are $$2:1$$ and the odds in favor of the price remaining the same are $$1:3$$. The probability that the price of the stock will go down during the next week, is 

A bag contains $$17$$ tickets numbered $$1$$ to $$17$$. A ticket is drawn and replaced, then one more ticket is drawn and replaced. Probability that first drawn number is even and second is odd, is

An $$MBM$$ applies for a job in two firms $$X$$ and $$Y$$. The probability of his being selected in firm $$X$$ is $$0.7$$ and being rejected at $$Y$$ is $$0.5$$. The probability of at least one of his applications being rejected is $$0.6$$. The probability that he will be selected in one of the firms, is

If A, B and C are three events such that $$P(B)=\dfrac {3}{4}, P(A\cap B\cap C')=\dfrac {1}{3}$$ and $$P(A'\cap B\cap C')=\dfrac {1}{3}$$, then $$P(B\cap C)$$ is equal to

The probability that at least one of $$A$$ and $$B$$ occurs is $$0.6$$ and probability that they occur simultaneously is $$0.3$$, then $$P(A')+P(B')$$ is:

What is the probability that a leap year has $$53$$ Sundays?

A die is thrown twice. What is the probability that
$$(i)$$ 3 will not come up either time?
$$(ii)$$ 6 will come up at least once?

The probabilities of three events $$A,B$$ and $$C$$ are $$P\left( A \right) =0.6,P\left( B \right) =0.4,P\left( C \right) =0.5$$,also 
$$P\left( A\cup B \right) =0.8,P\left( A\cap C \right) =0.3,P\left( A\cup B\cup C \right) \ge 0.85,P\left( A\cap B\cap C \right) =0.2$$ 
and $$P\left( B\cap C \right) ={ p }_{ 1 }$$. Then