Probability practice · Easy

The probability that out of 10 persons, all born in June, at least two have the same birth day is

Three numbers are chosen at random (without replacement) from the numbers $1,2, \ldots 20$. The probability that the numbers are not consecutive are

If two coins are tossed five times, then the probability of getting 5 heads and 5 tails is

The mode of the binomial distribution for which mean and standard deviation are 10 and $\sqrt 5 \;$ respectively, is

If the letters of the word PROBABILITY are written down at random in a row, the probability that two Bs are together is

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

A card is drawn from a pack of cards. The probability that the card will be a queen or a heart, is

Which one of the following is not correct?

All the heart cards are taken out from a pack of playing cards. From these cards, cards are drawn one by one without replacement till the ace of hearts comes. The probability that ace comes in the 4th draw is

Two events $E$ and $F$ are independent. If $P(E)=0.3$, $P(E \cup F)=0.5$, then $P(E \mid F)-P(F \mid E)$ equals

The probability that a randomly chosen one-one function from the set $\{a, b, c, d\}$ to the set $\{1,2,3$, $4,5\}$ satisfies $f(a)+2 f(b)-f(c)=f(d)$ is :

A dice is thrown 100 times, getting an even number is considered a success. The variance of the number of successes is

A box contains 10 good articles and 6 with defects, one article is chosen at random. What is the probability that it is either good or has a defect?

Unbiased die is thrown, probability that outcome is greater than 4, is

Four persons $A, B, C, D$ are to speak at a function along with 6 others. If they all speak in random order, the probability that $A$ speaks before $B, B$ before $C, C$ before $D$ is

If the probability that $A$ and $B$ will die with in a year are $p$ and $q$ respectively, then the probability that only one of them will be alive at the end of the year is

Let $A$ and $B$ be two independent events such that $P\left( A \right) = \frac{1}{3}$ and $P\left( B \right) = \frac{1}{6}.$ Then, which of the following is TRUE?

An unbiased coin is tossed fixed number of times. If the probability of getting 4 heads equals the probability of getting 7 heads, then the probability of getting 2 heads is

Three numbers are chosen at random from the numbers $1,2, \ldots 20$. The probability that the arithmetic mean of these numbers is 4 is

Three persons $\mathrm{P}, \mathrm{Q}$ and $\mathrm{R}$ independently try to hit a target. If the probabilities of their hitting the target are $\frac{3}{4}, \frac{1}{2}$ and $\frac{5}{8}$ respectively, then the probability that the target is hit by $\mathrm{P}$ or $\mathrm{Q}$ but not by $\mathrm{R}$ is :

Two cards are drawn one by one at random from a pack of 52 cards. The prohahility that both of them are king, is

Two cards are drawn one by one from a pack of cards. The probability of getting first card an ace and second a coloured one is (before drawing second card first card is not placed again in the pack)

Three numbers are chosen from 1 to 30. The probability that they are not consecutive is

In a class of 80 students numbered 1 to 80 , all odd numbered students opt of Cricket, students whose numbers are divisible by 5 opt for Football and those whose numbers are divisible by 7 opt for Hockey. If the number of students who do not opt any of the three games is $n$, then $\frac{n}{4}$ is equal to

Three numbers are chosen at random from numbers 1 to 30 . The probability that the minimum of the chosen numbers is 9 and maximum is 25 , is

Two squares are chosen at random on a chessboard. If $p$ denotes the probability that they have exactly one side in common, then $144 p$ is

If $A=\{x: x=4 n+1, n \leq 5, n \in N\}$ and $B\{3 n: n \leq 8$, $n \in N\}$, then find $(A-(A-B))$.

Events $A, B, C$ are mutually exclusive events such that $P(A)=\frac{3 x+1}{3}, P(B)=\frac{1-x}{4}$ and $P(C)=\frac{1-2 x}{2}$. The set of all possible values of $x$ are in the interval

One hundred identical coins, each with probability $p$ of showing heads are tossed once. If $0 < p < 1$ and the probability of heads showing on 50 coins is equal to that of heads showing on 51 coins, the value of $p$, is

A random variable $X$ has poisson distribution with mean 2. Then, $P(X > 1.5)$ equals