CUET Mathematics: AlgebraProbability. Free, no login required.

A die is rolled. If the outcome is an odd number, then the probability that the number is prime, is:

If $A$ and $B$ are two events such that $P(\overline{A} \cup \overline{B}) = \dfrac{2}{3}$ and $P(A \cup B) = \dfrac{5}{9}$, then which of the following are TRUE?

A. $P(A \cap B) = \dfrac{1}{3}$

B. $P(A \cup B) + P(A \cap B) = \dfrac{7}{9}$

C. $P(A) + P(B) = \dfrac{2}{9}$

D. $P(\overline{A}) + P(\overline{B}) = \dfrac{10}{9}$

Choose the correct answer from the options given below:

In a factory of fans, machine A, B and C manufacture respectively 20%, 40% and 40% of total fans. Out of their output 2, 3 and 5 percent are defective fans respectively. A fan is drawn at random from the products then the probability that the drawn fan is defective is:

Match the LIST-I with LIST-II

Choose the correct answer from the options given below:

A letter is known to have come either from LONDON or CLIFTON. On the envelop just two consecutive letter 'ON' are visible. The probability that the letter has come from LONDON is:

If the mean and variance of a binomial distribution are 4 and 3 respectively, then the probability of getting exactly 5 successes in the distribution is:

A random variable X has the following probability distribution:

Then, which of the following are correct ?

A. $k = 0.1$

B. $P(X<3) = 0.3$

C. $P(0<X<3) = 0.8$

D. $P(X>6) = 0.17$

Choose the correct answer from the options given below:

Let X denote the number of hours a person watches television during a randomly selected day. The probability that X can take the value $x_i$, has the following form, where $k$ is some unknown constant.

$P(X=x_i) = \begin{cases} 0.5 & \text{if } x_i=0 \\ kx_i & \text{if } x_i=1 \\ k(4-x_i) & \text{if } x_i=2 \text{ or } 3 \\ 0 & \text{otherwise} \end{cases}$

The probability that the person watches at most 2 hours of television on a selected day is :

The probability distribution table of a random variable X is given below.

If $E(X) = \dfrac{3}{2}$, then the values of a and b are:

Probability of solving a specific problem independently by A and B are $\frac{1}{2}$ and $\frac{1}{3}$ respectively, then which of the following are True?

[where P(X) denotes the probability of an event X]

(A) P(Problem is solved) = $\frac{2}{3}$

(B) P(Exactly one of them solves the problem) = $\frac{1}{2}$

(C) P(Both of them solve the problem) = $\frac{5}{6}$

(D) P(Atmost one solves the problem) = $\frac{5}{6}$

Choose the correct answer from the options given below:

If A and B are two independent events such that P(A) = 1/3, $P(A\cup B) = 3/5$ and P(B) = p, then which of the following are true?

(A) The value of p is $\frac{2}{5}$

(B) $P(A\cap B) = \frac{2}{15}$

(C) $P(B/A) = \frac{1}{3}$

(D) $P(A/B) = \frac{3}{5}$

Choose the correct answer from the options given below:

A pair of dice is thrown, then the probability of getting a sum of 7, is

A man is known to speak truth 4 out of 5 times. A coin is tossed. He reports that a head appears. The probability that actually there was a head, is

If two cards are drawn at random without replacement from a pack of 52 playing cards, then the probability that both the cards are red, is

A random variable X has the following probability distribution:

Which of the following are TRUE?

(A) P(X < 3) = 0.8

(B) P(X > 4) = 0.2

(C) The value of z is 0.1

(D) $P(3\le X<5) = 0.31$

Choose the correct answer from the options given below:

A box has 5 blue and 4 red balls. One ball is drawn at random and not replaced. Its colour is also not noted, then another ball is drawn at random. The probability of second ball being red is

If E and F are two events such that P(E) = 0.8, P(F) = 0.7 and P(E ∩ F) = 0.6 then $P(\bar{E}/\bar{F})$ is:

If A and B are two independent events such that P(A) = 0.5, P(B) = 0.3 then

Match the LIST-I with LIST-II

Choose the correct answer from the options given below:

A bag contains 17 tickets numbered from 1 to 17. A ticket is drawn, and then another ticket is drawn without replacing the first one. Then the probability that both the tickets show at least one even number, is

Probabilities of solving a specific mathematical problem independently by three students are $\frac{1}{2},\frac{1}{3}$ and $\frac{1}{4}$. If all the three students try to solve the problem independently, the probability that the problem is solved, is:

A company manufactured a product through 4 units. A, B, C and D. The probability that a product is manufactured are $\frac{3}{10},\frac{1}{5},\frac{1}{10}$ and $\frac{2}{5}$ by units A, B, C and D respectively. The probability that it will be defective are $\frac{1}{4},\frac{1}{3}$ and $\frac{1}{12}$ if it is produced by A, B, C respectively and there is no defective from unit D. A product is chosen, it is found to be defective.

Match the LIST-I with LIST-II

Choose the correct answer from the options given below:

If $P(B) = \frac{2}{5}, P(A \cup B) = \frac{3}{5}, P(A \cap B) = \frac{3}{10}$ then $P(A/B) + 2P(B/A)$ equals

If A, B and C are three independent events such that P(A)=P(B)=P(C)=x, then P(at least two of A, B, C occur) =

If A and B are two events such that $A \neq \emptyset$, B $\neq \emptyset$, then which of following is/are TRUE:

A. $P(B/A)=P(A).P(B)$

B. $P(B/A)=\frac{P(A\cap B)}{P(A)}$

C. $P(A'/B')=\frac{1-P(A\cup B)}{1-P(B)}$

D. $P(B/A).P(A/B)=2$

Choose the correct answer from the options given below:

An insurance company insured 200 scooter drivers, 400 car drivers and 600 Truck drivers. The probability of an accident involving scooter driver, car driver and truck driver are 0.01, 0.03 and 0.15 respectively. One of the insured person meets an accident, then the probability that he is a truck driver is:-

A box contains 3 red and 2 black balls and another box contains 2 red and 4 black balls. One box chosen at random. From the selected box one ball is drawn. The probability of getting a red ball is

Ten cards are numbered from 1 to 10. A and B are playing a game by drawing a card, alternately, with replacement, till one gets a prime number then the probability of B's winning if A started the game is

If A and B are event such that $P(A)=\dfrac{1}{2}$, $P(B)=p$ and $P(A \cup B)=\dfrac{3}{5}$ then which of following statements is/are TRUE?

(A) Events A and B are independent if $p=\dfrac{1}{5}$

(B) Events A and B are independent if $p \in (0,1) \sim \left\{\dfrac{1}{5}\right\}$

(C) Events A and B are independent then $P(A \cap B)=\dfrac{1}{10}$

(D) Event A and B are independent then $P(A \cap B)=\dfrac{9}{10}$

Choose the correct answer from the options given below:

Bag A contains 3 red and 5 white balls and bag B contains 4 red and 4 white balls. A bag is selected at random, and a ball is drawn. Then the probability of getting a red ball is:

Let A and B be two independent events such that $P(A)=k$, $P(B)=2k$ and probability of occurrence of exactly one of them is $\dfrac{5}{9}$. Then the value(s) of $k$ is/are: