Probability practice · Easy

If a bag contains 50 tickets, numbered $1,2,3, \ldots, 50$ of which five are drawn at random and arranged in ascending order of magnitude $\left( {{x_1} < {x_2} < {x_3} < {x_4} < {x_5}} \right)$. The probability that $x_3=30$, is

The probability that a leap year selected at random will contain either 53 Thursdays or 53 Fridays, is

If $A$ and $B$ are two events, the probability that exactly one of them occurs is not given by

A police-man fires six bullets on a dacoit. The Probability that the dacoit will be killed by one bullet is 0.6 . The Probability that dacoit is still alive is

Four fair dice $D_1, D_2, D_3$ atd $D_4$, each having six faces numbered 1,2,3,4,5 and 6 are rolled simultaneously. The probability that $D_4$ shows a number on one of $D_1, D_2$ and $D_3$ is

The probability that the 13th day of a randomly chosen month is a Friday, is

Let $A$ and $B$ be two events such that $P(B \mid A)=\frac{2}{5}, P(A \mid B)=\frac{1}{7}$ and $P(A \cap B)=\frac{1}{9}$, Consider $(S 1) P\left(A^{\prime} \cup B\right)=\frac{5}{6},(S 2) P\left(A^{\prime} \cap B^{\prime}\right)=\frac{1}{18}$. Then

Let $A = \left\{ {1,\;3,\;5,\;7,\;9} \right\},\;B = \left\{ {2,\;4,\;6,\;8} \right\}.$ If a cartesian product $A \times B$, if chosen at random, the probability of $a + b = 9$ is

Let ${A}=[2,3,4, \ldots, 20]$. A number is chosen at random from the set ${A}$ and it is found to be a prime number. The probability that it is more than 10 is

A doctor is called to see a sick child. The doctor knows (prior to the visit) that $90 \%$ of the sick children in that neighbourhood are sick with the flue, denoted by $F$, while $10 \%$ are sick with the measles, denoted by M. A well-known symptom of measles is a rash, denoted by $R$.
The probability of having a rash for a child sick with the measles is $0.95$. However, occasionally children with the flue also develop a rash with conditional probability $0.08$. Upon examination the child, the doctor finds a rash, then the probability that the child has the measles, is

Write the set $A=\{x: x$ is a positive prime $< 10\}$ in the tabular form

Let $A$ and $B$ be the sets $\{1,2, \ldots 10\}$ and $\{1,2, ...20\}$ respectively. A function is selected randomly from $A$ to $B$ the probability that the function is non-decreasing is

Six teams play a match with each other. The probability that neither a team win all the matches nor a team loose all the matches is

Three coins are tossed, then what is the probability that at least two heads appears on upper face?

An urn contains nine balls of which three are red, four are blue and two are green. Three balls are drawn at random without replacement from the urn. The probability that the three balls have different colours, is

$n(\geq 3)$ persons are sitting in a row. Two of them are selected at random. The probability that they are not together is

A die is rolled thrice, the probability of getting a larger number each time than the previous number, is

Entries of a $2 \times 2$ determinant are chosen from the set $\{-1,1\}$. The probability that determinant has zero value is

India plays a two ODI matches each with Australia and Pakistan. The probability of India getting points 0, 1, 2 are 0.45, 0.05, 0.50. The probability of India getting at least 7 points in the series is

The mean and variance of a random variable $X$ having a binomial distribution are 4 and 2 respectively, then $P\left( {X = 1} \right)$ is

A draws two cards at random from a pack of 52 cards. After returning them to the pack and shuffling it, B draws two cards at random. The probability that their draws contain exactly one common cards is

Five horses are in a race. Mr. A selects two of the horses at random and bets on them. The probability that Mr. A selected the winning horse is

In a college, 25% of the boys and 10% of the girls offer Mathematics. The girls constitute 60% of the total number of students. If a student is selected at random and is found to be studying Mathematics. The probability that the student is a girl is

A card is drawn from a pack of 52 playing cards. The card is replaced and the pack is reshuffled. If this is done six times, the probability that 2 hearts, 2 diamonds and 2 black cards are drawn is

Let A, B, C be three mutually independent events.

Consider the two statements $\mathrm{S}_1$ and $\mathrm{S}_2$

$\mathrm{S}_1: \mathrm{A}$ and $B \cup C$ are independent

$\mathrm{S}_2: \mathrm{A}$ and $B \cap C$ are independent, then

If birth to male child and birth to female child are equal-probable, then what is the probability that at least one of the three children born to a couple is male?

If $A$ and $B$ are two independent events, the probability that both $A$ and $B$ occur is $1/8$ and the probability that neither of them occurs is $3/8.$ The probability of the occurrence of $A$, is

Three different numbers are selected at random from the set $A=\{1,2,3, \ldots, 10\}$. The probability that the product of two of the numbers is equal to third, is

If $A$ and $B$ are mutually exclusive events with $P\left( A \right) = \frac{1}{2} \times P\left( B \right)$ and $A \cup B = S,$ (total sample space) then $P\left( A \right)$ is equal to

$A$ and $B$ are the independent events. The probability that both occur simultaneously is $\frac{1}{6}$ and the probability that neither occur is $\frac{1}{3}$. The probability of occurrence of the events $A$ and $B$ is