Probability practice · Mixed difficulty

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

Two dice are thrown $n$ times in succession. The probability of obtaining a double six at least once 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

Throwing a biased die, a person will get 5 rupees if he throws the number 5 and will get 8 rupees for any
other number, then the expected income (in Rupees) per throw is (it is given that the number 5 will appear
5 times as frequently as any other number)

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

Two numbers $a$ and $b$ are chosen at random from the set $\{1,2,3, \ldots, 3 n\}$. The probability that $a^2-b^2$ is divisible by 3 , is

An anti-aircraft gun can take a maximum of four shots at any plane moving away from it. The probabilities of hitting the plane at the 1st, 2nd, 3rd and 4th shots are 0.4, 0.3, 0.2 and 0.1 respectively. What is the probability that at least one shot hits the plane?

Let ${R}$ be the region containing all the points within or on the sides of an equilateral triangle. A point $P$ is randomly selected from the region $R$, the probability that $P$ lies near to internal angle bisector than any of the sides is equal to

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

$A$ is a set containing n elements. A subset $P$ of $A$ is chosen at random. The set $A$ is reconstructed by replacing the elements of $P$. A subset $Q$ is again chosen at random. The Probability that $P \cup Q=A$, 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

Among 15 players, 8 are batsman and 7 are bowlers. The probability that a team is chosen of 6 batsman and 5 bowlers, 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 ${X}$ and ${Y}$ are the independent random variables ${B}\left(5, \frac{1}{2}\right)$ and ${B}\left(7, \frac{1}{2}\right)$, then ${P}({X}+{Y} \geq 1)=$

$A$ is a set containing n elements. A subset $P$ of $A$ is chosen at random. The set $A$ is reconstructed by replacing the elements of $P$. A subset $Q$ is again chosen at random. The Probability that $P \cap Q$ contain just one element, is

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

Minimum number of times a fair coin must be tossed so that the probability of getting atleast one head is more than 99% is