Probability practice · Easy

Let $A$ and $B$ be two events such that $P(\overline{A \cup B})=\frac{1}{6}, P(A \cap B)=\frac{1}{4}$ and $P(\bar{A})=\frac{1}{4}$, where $\bar{A}$ stands for complement of event $A$. Then events $A$ and $B$ are

A bag contains 4 red and 6 black balls. A ball is drawn at random from the bag, its colour is observed and this ball along with two additional balls of the same colour are refurned to the bag. If now a ball is drawn at random from the bog, then the probability this ball drawn is red, is

The probability that the three cards drawn from a pack of 52 cards, are all black, is

The odds that $A$ speaks the truth are $3: 2$ and the odds that $B$ speaks the truth are $5: 3$. The percentage of cases they are likely to contradict each other on an identical point is

The mean and variance of a binomial variable $X$ are 2 and 1 respectively. The probability that $X$ takes values greater than 1, is

A biased coin with probability $p, 0 < p < 1$, of heads is tossed until a head appears for the first time. If the probability that the number of tosses required is even is $2 / 5$, then p equals

Let $A$ and $B$ be two events such that the probability that exactly one of them occurs is $\frac{2}{5}$ and the probability that $A$ or $B$ occurs is $\frac{1}{2}$, then the probability of both of them occur together is

An insurance salesman sells policies to 5 men, all of identical age and in good health. The probability that a man of this particular age will be alive after 30 years is 2/3. The probability that after the lapse of 30 years all the five persons will be alive, is

Each of $a$ and $b$ can take values 1 or 2 with equal probability. The probability that the equation $a x^2+b x+1=0$ has real roots, is equal to

If the sides of a triangle are decided by the throw of a single dice thrice, the probability that triangle is of maximum area given that it is an isosceles triangle, is

A man alternately tosses a coin and throws a dice beginning with the coin. The probability that he gets a head before he gets 5 or 6 in the dice is

A person writes 4 letters and addresses 4 envelopes. If the letters are placed in the envelopes at random, the probability that not all letters are placed in correct envelopes is