Probability Tes...

Let $${ U }_{ 1 }$$ and $${ U }_{ 2 }$$ be two urns such that $${ U }_{ 1 }$$ contains 3 white and 2 red balls, and $${ U }_{ 2 }$$ contains only 1 white ball. A fair coin is tossed. If head appears then 1 ball is drawn at random from $${ U }_{ 1 }$$ and put into $${ U }_{ 2 }.$$ However, if tail appears then 2 balls are drawn at random from $${ U }_{ 1 }$$ and put into $${ U }_{ 2 }.$$ Now 1 ball is drawn at random from $${ U }_{ 2 }.$$
The probability of the drawn ball from $${ U }_{ 2 }$$being white is-

Three coins are thrown simultaneously 60 times, with the following frequencies: 

The events  $$A$$  and  $$B$$  are mutually exclusive, so

The slope of given line is 

An unbiased coin is tossed n times. Let X denote the number of times head occurs. If P(X=4), P(X=5) and P(X=6) are in AP, then the value of n can be

The p.m.f.of a r.v. X is as follows ;
$$P(X=0)=3{ K }^{ 3 }\quad ,\quad P(X=1)=4K-10{ K }^{ 2 },\quad P(X=2)=5K-1,\quad P(X-x)=0$$ for any other value of x. then k is equal to 

If a number is selected at random, then getting a prime or composite number is a ________ event.

Ravi and Rashmi are each holding 2 red cards and 2 black cards (all four red and all four black cards are identical). Ravi picks a card at random from Rashmi, and then Rashmi picks a card at random from Ravi. This process is repeated a second time. Let p be the probability that both have all 4 cards of the same colour. Then p satisfies

A fair die is tossed repeatedly until a 6 is obtained. Let X denote the number  of tosses required.

Two cards are drawn from a well shuffled deck of 52 playing cards with replacement.
The probability, that both cards are queen, is