Probability practice · Easy

The probability of having at least one tail in 4 throws with a coin, is

Five persons $A,\,\;B,\,\;C,\;\,D$ and $E$ are in queue of a shop. The probability that $A$ and $E$ always together, is

Suppose $n(\geq 3)$ persons are arranged in a row. The probability that two particular persons are not together is

An article manufactured by a company consits of two parts $A$ and $B$. In the processs of manufacutre of part $A$, 9 out of 100 are likely to be defective. Similarly 5 out of 100 are likely to be defective in the manufacture of part $B$. The probability that the assembled part will not be defective, is

If a triangle is formed by choosing the vertices of 10 sided regular polygon. Then probability that triangle has exactly one side in common with the polygon, is

A fair die is tossed repeatedly until a six is obtained. Let $X$ denote the number of tosses required. The probability that $X \geq 3$ equals

A rifleman is firing at a distant target and has only $10 \%$ chance of hitting it. The least number of rounds, he must fire in order to have more than $50 \%$ chance of hitting it at least once, is

A fair die is rolled. The probability that the first time 1 occurs at the even throw is

If $A$ and $B$ are two independent events such that $P(\bar{B})=\alpha P(\bar{A})=\frac{7}{10}, P(\bar{B})=\alpha$ and $P(A \cup B)=\frac{8}{10}$, then $\alpha$, is

Let $A, B, C$ be pairwise independent events with $P(C)>0$ and $P(A \cap B \cap C)=0$. Then, $P\left(A^c \cap B^c / C\right)$ is equal to

$'X'$ speaks truth in $60 \%$ and ' $Y$ ' in $50 \%$ of the cases. The probability that they contradict each other while narrating the some incident, is

An urn contains 5 red and 2 green balls. A ball is drawn at random from the urn. If the drawn ball is green, then a red ball is added to the urn; if the drawn ball is red, then a green ball is added to the urn the original ball is not returned to the urn. Now, a second ball is drawn at random from it. The probability that the second ball is red, is

A box contains 10 mangoes out of which 4 are rotten. 2 mangoes are taken out together. If one of them is found to be good, the probability that the other is also good is

$2 n$ boys are randomly divided into two subgroups containing $n$ boys each. The probability that the two tallest boys are in different groups is

If the standard deviation of the binomial distribution $(q+p)^{16}$ is 2, then mean of the distribution is

If the mean and variance of a binomial variate $X$ are 2 and 1 respectively, then the probability that $X$ takes a value greater than 1, is

While shuffling a pack of 52 playing cards. Unfortunately 4 cards are dropped on the ground it is known that 2 out of 4 are spades. What is the probability that all dropped 4 are spades?

If four positive integers are taken at random and multiplied together, then the probability that the last digit is 1, 3, 7 or 9 is

The probability that the birth days of six different persons will fall in exactly two calendar months is

A three digit number, which is a multiple of 11, is chosen at random. Probability that the number so chosen is also a multiple of 9, is equal to

An integer is chosen at random from the first 200 positive integers. The probability that the integer chosen is divisible by 6 or 8 is

Let $S$ be the sample space of all five digit numbers. It $p$ is the probability that a randomly selected number from $S$, is multiple of 7 but not divisible by 5 , then $9 p$ is equal to

If $n(\mathrm{~A})=1000, n(\mathrm{~B})=500$ and if $n(\mathrm{~A} \cap \mathrm{B}) \geq 1$ and $n(\mathrm{~A} \cup \mathrm{B})=p$, then

A die is thrown. Let $A$ be the event that the number obtained is greater than 3. Let B be the event that the number obtained is less than 5. Then, $P(A \cup B)$ is

$A, B, C$ are three mutually exclusive and exhaustive events associated with a random experiment. If ${P}({B})$ $=\frac{3}{2} {P}({A})$ and ${P}({C})=\frac{1}{2} {P}({B})$, then ${P}({A})=$

Six dice are thrown simultaneously. The probability that exactly three of them show the same face and remaining three show different faces, is

A class consists of 80 students, 25 of them are girls. If 10 of the students are rich and 20 of the students are fair complexioned, then the probability of selecting a fair complexioned rich girl from the class (assuming three traits as independent) is

If $A$ and $B$ each toss three coins. The probability that both get the same number of heads is

The probability that when 12 balls are distributed among three boxes, the first will contain three balls is,

Let $A$ be a set consisting of $n$ elements. The probability of selecting two subsets $P$ and $Q$ of set $A$ such that $Q=\bar{P}$, is