Probability Tes...

If the integers $$'m'$$ and $$'n'$$ are chosen at random from $$1$$ to $$100$$ then the probability that $$7^{m}+7^{n}$$ is divisible by $$5$$ is ?

Consider 5 independent bernoulli's trials each with probability p of success. If the probability of one failure is greater than or equal to $${{31} \over {32}}$$, then p lies in the interval

A  fair dice is rolled three times, then the probability of getting a number larger than the previous number is 

Two non-negative integers are chosen at random from the set of non-negative integers with replacement. The probability that the sum of their squares is divisible by $$10$$ is 

The value of $${P}_{n}$$ is equal to

If the integers $$m$$ and $$n$$ are chosen at random from $$1$$ to $$100$$ then the probability that $${7}^{m}+{7}^{n}$$ is divisible by $$5$$ is  ?

Which of the following is not true?

A boy has a collection of blue and green marbles. The number of blue marbles belong to the sets $${2,3,4,13}$$. If two marbles are chosen simultaneously and at random from his collection, then the probability that they have different colour is $$1/2$$. Possible number of blue marbles is:

Two numbers x and y are chosen at random without replacement from the first $$30$$ natural numbers. The probability that $$x^2-y^2$$ is divisible by $$3$$ is?

Let $$A$$ and $$B$$ be events such that $$P(\overline{A})=\dfrac{4}{5}, P(B) = \dfrac{1}{3}, P\left(\dfrac{A}{B}\right) = \dfrac{1}{6}$$, then: