Probability Tes...

The contents of urn I and II are as follows:
Urn I: 4 white and 5 black balls
Urn II: 3 white and 6 black balls
One urn is chosen at random and a ball is drawn and its colour is noted and replaced back to the urn. Again a ball is drawn from the same urn colour is noted and replaced. The process is repeated 4 times and as a result one ball of white colour and 3 of black colour are noted. Find the probability the chosen urn was I.

The ratio of the number of trucks along a highway, on which a petrol pump is located, to the number of cars running along the same highway is 3 : 2. It is known that an average of one truck in thirty trucks and two cars in fifty cars stop at the petrol pump to be filled up with the fuel. If a vehicle stops at the petrol pump to be filled up with the fuel, find the probability that it is a car

In a series of 3 independent trials, the probability of exactly 2 success is 12 times as large as the probability of 3 successes. The probability of a success in each trail is

A signal which can be green or red with probability $$\displaystyle \frac{4}{5}$$ and $$\displaystyle \frac{1}{5}$$, respectively, is received at station A and then transmitted to station B. The probability of each station receiving the signal correctly is $$\displaystyle \frac{3}{4}$$. If the signal received at station B is green, then the probability that the original signal was green is

There are two urns. There are $$m$$ white & $$n$$ black balls in the first urn and $$p$$ white & $$q$$ black balls in the second urn. One ball is taken from the first urn & placed into the second. Now, the probability of drawing a white ball from the second urn is

One ticket is selected at random from $$100$$ tickets numbered $$100,01, 02, .... 98, 99.$$  If $$x_{1}$$ and $$x_{2} $$ denotes the sum and product of the digits on the tickets, then $$ P((x_{1} =9)/(x_{2} =0))$$ is equal to

A fair coin is tossed five times. If the out comes are $$2$$ heads and $$3$$ tails (in some order), then what is the probability that the fourth toss is a head?

A boy has 20% chance of hitting at a target. Let p denote the probability of hitting the target for the first time at the nth trial. If $$p$$ satisfies the inequality $$ 625p^{2} - 175p + 12 < 0$$ then value of $$n$$ is

When two dice are rolled, find the probability of getting a greater number on the first die than the one on the second, given that the sum should equal 8.

In a set of $$10$$ coins, $$2$$ coins are with heads on both the sides. A coin is selected at random from this set and tossed five times. If all the five times, the result was heads, find the probability that the selected coin had heads on both the sides.