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If E and F are two events such that $P(E \cup F)=P(E)$, then

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

A green and a yellow dice are rolled in order, then the probability that a sum greater than 9 is

Given that the two numbers appearing on throwing 2 dice are different, the probability of the event " sum of number on the dice is 4 " is

Bag I contains 3 red and 4 black balls while Bag II contains 5 red and 6 black balls. One ball is drawn at random from one of the bags and it is found to be red. then the probability that it was drawn from Bag I is

A committee of 4 students is selected at random from a group consisting of 8 girls and 4 boys. Given that there is at least one boy in the committee, the probability that there are exactly 2 boys in the committee is

For a biased die, the probabilities of outcomes are given as under.

$P(1)=P(2)=\dfrac{2}{10}, P(3)=P(5)=P(6)=\dfrac{1}{10}, P(4)=\dfrac{3}{10}$.

The die is thrown two times. Let A and B be events defined as

A is getting same number each time and

B is getting a total of 10 or more on die ,

then which one of the following is TRUE?

A random variable $X$ has the following probability distribution:

Match the LIST-I with LIST-II

Choose the correct answer from the options given below:

Let $P(A) = 0.4$, $P(B) = k$, $P(A\cup B) = 0.6$. If A and B are independent events, then the value of 'k' is:

For two events A and B, if $P(A) = 0.6$, $P(B) = 0.5$ and $P(A\cup B) = 0.8$. Then which of the following statements are TRUE ?

A. $P(A\cap B) = 0.3$.

B. A and B are independent events.

C. $P(A'\cap B') = 0.2$.

D. A and B are mutually exclusive events.

Choose the correct answer from the options given below:

A four digit number is formed by using the digits 1, 2, 4 and 5 with no repetition. The probability that the number is divisible by 5, is

Bag A contains 3 red and 4 black balls, and Bag B contains 5 red and 'n' black balls. One ball is drawn at random from one of the bags and it is found to be red. If the probability that it was from bag B is 35/68, then the value of 'n' is:

If $P(A) = \dfrac{3}{10}, P(B) = \dfrac{3}{4}$ and $P(A\cap B) = \dfrac{1}{5}$, then $P(B\mid A)$ is equal to:

A bag contains 8 red and 7 black balls. Two balls are drawn at random. The probability that both the balls are of the same colour is:

Two numbers are selected at random from the integers 1 through 19. If the sum is even, then the probability that both are odd numbers is:

Urn A contains 1 white, 2 black and 3 red balls, Urn B contains 2 white, 1 black and 1 red ball and Urn C contains 4 white, 5 black and 3 red balls. One Urn is chosen at random and two balls are drawn. If it is found that there is one white and one red, Then the probability that they come from A is:

If A and B are two independent events such that $P(A) = \frac{4}{7}$ and $P(B) = \frac{2}{7}$ then $P(\overline{A} \cap \overline{B})$ equals

Two dice are thrown simultaneously. If X denotes the number of sixes appearing on two dice, then which of the following are correct?

(A) $P(X=0)=\frac{1}{36}$

(B) $P(X=1)=\frac{10}{36}$

(C) $P(X=1)+P(X=0)=\frac{35}{36}$

(D) $P(X=1)+P(X=2)=\frac{11}{36}$

Choose the correct answer from the options given below:

Five bad apples are mixed with 15 good apples accidently. Let the random variable X be the number of bad apples in a draw of two apples, then mean of X is

A random variable X has the following probability distribution:

The value of $P(X\ge 3)$ is

A pair of dice is thrown then probability of getting sum of numbers on dice is '8', is:

Let E and F are two independent events such that $P(E)=0.35$ and $P(E\cup F)=0.60$ then which of following statements are TRUE?

(A) $P(F)=\frac{5}{13}$

(B) $P(E|\overline{F})=0.35$

(C) $P(E|\overline{F})=0.65$

(D) $P(\overline{E}|\overline{F})=0.65$

Choose the correct answer from the options given below:

A school has to send the report cards of 3 students, but the cleark has not paid attention to match the address on the envelope with the student report card is: The probability that exactly one of the students received his or her own report card is:

Three bags contain a number of red and white balls as follows:

Bag I: 3 red balls

Bag II: 2 red balls and 1 white ball

Bag III: 3 white balls

The probability that bag $i$ will be chosen, and a ball is selected from it is $\frac{i}{6}, i=1,2,3$. The probability that a red ball is selected is equal to:

Bag I contains 2 red and 3 blue balls and bag II contains $\alpha$ red and 5 blue balls. One ball is drawn at random from one of the bags and is found to be blue. If the probability that it was drawn from bag II is $\frac{25}{52}$, then $\alpha$ is equal to:

Two dice are thrown simultaneously. If X denotes the number of sixes, then the mean of X is :

Match List-I with List-II

Choose the correct answer from the options given below:

The sum and the product of the mean and variance of binomial distribution are 1.8 and 0.8 respectively. The probability of atleast one success is:

If A and B are two events such that $P(A) = \dfrac{3}{10}, P(B) = \dfrac{2}{5}$ and $P(A \cup B) = \dfrac{3}{5}$, then $P(B|A) + P(A|B)$ is:

Let A and B be two events such that $P(A \cap B) = 0$ then $P(A|(A \cup B))$ is equal to: