Probability Tes...

A number is chosen at random from among the 1st 50 natural numbers. The probability that the number chosen is either a prime number or a multiple of 5 is

A lot contains $$50$$ defective and $$50$$ non-defective bulbs. Two bulbs are drawn at random, one at a time, with replacement. The events $$A, B, C$$ are defined as $$A = $$ {the first bulb is defective}, $$B =$$ {the second bulb is non defective}, $$C =$$ {the two bulbs are both defective or both non defective}, then which of the following statements is/are true?(1) $$A, B, C$$ are pair wise independent.(2) $$A, B, C$$ are independent.

Given two events A and B, if the odds against Aare 2 to 1, and those in favour of A$$\cup $$B are 3 to1, then

The probability of raining on day $$1$$ is $$0.2$$ and on day $$2$$ is $$0.3$$. The probability of raining on both the days is

The probability that atleast one of the events $$A, B$$ happens is $$0.6$$. If probability of their simultaneously happening is $$0.5$$, then $$P(\bar{A})+P(\bar{B})=$$

The probabilites of three events $$A,B$$ and $$C$$ are $$P\left( A \right) =0.6,P\left( B \right) =0.4$$ and $$P\left( C \right) =0.5$$. If $$P\left( A\cup B \right) =0.8,P\left( A\cap C \right) =0.3,P\left( A\cap B\cap C \right) =0.2$$ and $$P\left( A\cup B\cup C \right) \ge 0.85$$, then

If events $$A$$ and $$B$$ are independent and $$P(A)=0.15, P(A\cup B)=0.45$$, then $$P(B)=$$

If $$\displaystyle \frac{1-3p}{2},\frac{(1+4p)}{3},\frac{1+p}{6}$$ are the probabilities of three mutually exclusive and exhaustive events,then the set of all values of p is